Probabilistic reasoning US Medical PG Practice Questions and MCQs
Practice US Medical PG questions for Probabilistic reasoning. These multiple choice questions (MCQs) cover important concepts and help you prepare for your exams.
Probabilistic reasoning US Medical PG Question 1: A scientist in Chicago is studying a new blood test to detect Ab to EBV with increased sensitivity and specificity. So far, her best attempt at creating such an exam reached 82% sensitivity and 88% specificity. She is hoping to increase these numbers by at least 2 percent for each value. After several years of work, she believes that she has actually managed to reach a sensitivity and specificity much greater than what she had originally hoped for. She travels to China to begin testing her newest blood test. She finds 2,000 patients who are willing to participate in her study. Of the 2,000 patients, 1,200 of them are known to be infected with EBV. The scientist tests these 1,200 patients' blood and finds that only 120 of them tested negative with her new exam. Of the patients who are known to be EBV-free, only 20 of them tested positive. Given these results, which of the following correlates with the exam's specificity?
- A. 82%
- B. 90%
- C. 84%
- D. 86%
- E. 98% (Correct Answer)
Probabilistic reasoning Explanation: ***98%***
- **Specificity** measures the proportion of **true negatives** among all actual negatives.
- In this case, 800 patients are known to be EBV-free (actual negatives), and 20 of them tested positive (false positives). This means 800 - 20 = 780 tested negative (true negatives). Specificity = (780 / 800) * 100% = **98%**.
*82%*
- This value represents the *original sensitivity* before the scientist’s new attempts to improve the test.
- It does not reflect the *newly calculated specificity* based on the provided data.
*90%*
- This value represents the *newly calculated sensitivity* of the test, not the specificity.
- Out of 1200 EBV-infected patients, 120 tested negative (false negatives), meaning 1080 tested positive (true positives). Sensitivity = (1080 / 1200) * 100% = 90%.
*84%*
- This percentage is not directly derived from the information given for either sensitivity or specificity after the new test results.
- It does not correspond to any of the calculated values for the new test's performance.
*86%*
- This percentage is not directly derived from the information given for either sensitivity or specificity after the new test results.
- It does not correspond to any of the calculated values for the new test's performance.
Probabilistic reasoning US Medical PG Question 2: Group of 100 medical students took an end of the year exam. The mean score on the exam was 70%, with a standard deviation of 25%. The professor states that a student's score must be within the 95% confidence interval of the mean to pass the exam. Which of the following is the minimum score a student can have to pass the exam?
- A. 45%
- B. 63.75%
- C. 67.5%
- D. 20%
- E. 65% (Correct Answer)
Probabilistic reasoning Explanation: ***65%***
- To find the **95% confidence interval (CI) of the mean**, we use the formula: Mean ± (Z-score × Standard Error). For a 95% CI, the Z-score is approximately **1.96**.
- The **Standard Error (SE)** is calculated as SD/√n, where n is the sample size (100 students). So, SE = 25%/√100 = 25%/10 = **2.5%**.
- The 95% CI is 70% ± (1.96 × 2.5%) = 70% ± 4.9%. The lower bound is 70% - 4.9% = **65.1%**, which rounds to **65%** as the minimum passing score.
*45%*
- This value is significantly lower than the calculated lower bound of the 95% confidence interval (approximately 65.1%).
- It would represent a score far outside the defined passing range.
*63.75%*
- This value falls below the calculated lower bound of the 95% confidence interval (approximately 65.1%).
- While close, this score would not meet the professor's criterion for passing.
*67.5%*
- This value is within the 95% confidence interval (65.1% to 74.9%) but is **not the minimum score**.
- Lower scores within the interval would still qualify as passing.
*20%*
- This score is extremely low and falls significantly outside the 95% confidence interval for a mean of 70%.
- It would indicate performance far below the defined passing threshold.
Probabilistic reasoning US Medical PG Question 3: A 25-year-old man with a genetic disorder presents for genetic counseling because he is concerned about the risk that any children he has will have the same disease as himself. Specifically, since childhood he has had difficulty breathing requiring bronchodilators, inhaled corticosteroids, and chest physiotherapy. He has also had diarrhea and malabsorption requiring enzyme replacement therapy. If his wife comes from a population where 1 in 10,000 people are affected by this same disorder, which of the following best represents the likelihood a child would be affected as well?
- A. 0.01%
- B. 2%
- C. 0.5%
- D. 1% (Correct Answer)
- E. 50%
Probabilistic reasoning Explanation: ***Correct Option: 1%***
- The patient's symptoms (difficulty breathing requiring bronchodilators, inhaled corticosteroids, and chest physiotherapy; diarrhea and malabsorption requiring enzyme replacement therapy) are classic for **cystic fibrosis (CF)**, an **autosomal recessive disorder**.
- For an autosomal recessive disorder with a prevalence of 1 in 10,000 in the general population, **q² = 1/10,000**, so **q = 1/100 = 0.01**. The carrier frequency **(2pq)** is approximately **2q = 2 × (1/100) = 1/50 = 0.02**.
- The affected man is **homozygous recessive (aa)** and will always pass on the recessive allele. His wife has a **1/50 chance of being a carrier (Aa)**. If she is a carrier, she has a **1/2 chance of passing on the recessive allele**.
- Therefore, the probability of an affected child = **(Probability wife is a carrier) × (Probability wife passes recessive allele) = 1/50 × 1/2 = 1/100 = 1%**.
*Incorrect Option: 0.01%*
- This percentage is too low and does not correctly account for the carrier frequency in the population and the probability of transmission from a carrier mother.
*Incorrect Option: 2%*
- This represents approximately the carrier frequency (1/50 ≈ 2%), but does not account for the additional 1/2 probability that a carrier mother would pass on the recessive allele.
*Incorrect Option: 0.5%*
- This value would be correct if the carrier frequency were 1/100 instead of 1/50, which does not match the given population prevalence.
*Incorrect Option: 50%*
- **50%** would be the risk if both parents were carriers of an autosomal recessive disorder (1/4 chance = 25% for affected, but if we know one parent passes the allele, conditional probability changes). More accurately, 50% would apply if the disorder were **autosomal dominant** with one affected parent, which is not the case here.
Probabilistic reasoning US Medical PG Question 4: A mother presents to the family physician with her 16-year-old son. She explains, "There's something wrong with him doc. His grades are getting worse, he's cutting class, he's gaining weight, and his eyes are often bloodshot." Upon interviewing the patient apart from his mother, he seems withdrawn and angry at times when probed about his social history. The patient denies abuse and sexual history. What initial test should be sent to rule out the most likely culprit of this patient's behavior?
- A. Complete blood count
- B. Sexually transmitted infection (STI) testing
- C. Blood culture
- D. Urine toxicology screen (Correct Answer)
- E. Slit lamp examination
Probabilistic reasoning Explanation: ***Urine toxicology screen***
- The patient's presentation with **declining grades**, **cutting class**, **weight gain**, **bloodshot eyes**, and **irritability** are classic signs of **substance abuse** in an adolescent.
- A **urine toxicology screen** is the most appropriate initial test to detect common illicit substances, especially given the clear signs pointing towards drug use.
*Slit lamp examination*
- This test is used to examine the **anterior segment of the eye**, including the conjunctiva, cornea, iris, and lens.
- While the patient has **bloodshot eyes**, this specific test would be more relevant for ruling out ocular infections or injuries, not for diagnosing the underlying cause of systemic behavioral changes.
*Complete blood count*
- A **complete blood count (CBC)** measures different components of the blood, such as red blood cells, white blood cells, and platelets.
- A CBC is a general health indicator and while it can detect infections or anemia, it is not specific or sensitive enough to identify the cause of the behavioral changes described.
*Sexually transmitted infection (STI) testing*
- Although the patient denies sexual history, all adolescents presenting with certain risk factors or symptoms may warrant STI testing in a broader health assessment.
- However, in this scenario, the primary cluster of symptoms (poor grades, cutting class, bloodshot eyes, irritability) points more directly to substance abuse than to an STI.
*Blood culture*
- A **blood culture** is used to detect the presence of bacteria or other microorganisms in the bloodstream, indicating a systemic infection (sepsis).
- The patient's symptoms are not indicative of an acute bacterial bloodstream infection, and a blood culture would not be the initial test for the presented behavioral changes.
Probabilistic reasoning US Medical PG Question 5: A 26-year-old medical student comes to the physician with a 3-week history of night sweats and myalgias. During this time, he has also had a 3.6-kg (8-lb) weight loss. He returned from a 6-month tropical medicine rotation in Cambodia 1 month ago. A chest x-ray (CXR) shows reticulonodular opacities suggestive of active tuberculosis (TB). The student is curious about his likelihood of having active TB. He reads a study that compares sputum testing results between 2,800 patients with likely active TB on a basis of history, clinical symptoms, and CXR pattern and 2,400 controls. The results are shown:
Sputum testing positive for TB Sputum testing negative for TB Total
Active TB likely on basis of history, clinical symptoms, and CXR pattern 700 2100 2,800
Active TB not likely on basis of history, clinical symptoms, and CXR pattern 300 2100 2,400
Total 1000 4200 5,200
Which of the following values reflects the probability that a patient with a diagnosis of active TB on the basis of history, clinical symptoms, and CXR pattern actually has active TB?
- A. 1.4
- B. 0.50
- C. 0.70
- D. 0.88
- E. 0.25 (Correct Answer)
Probabilistic reasoning Explanation: ***0.25***
- This value represents the **positive predictive value (PPV)** for active TB based on the initial clinical assessment criteria (history, symptoms, CXR).
- PPV is calculated as the number of true positives (700) divided by the total number of individuals with a positive clinical diagnosis (700 + 2100 = 2800). So, 700 / 2800 = 0.25.
- **This answers the question**: the probability that someone with a clinical diagnosis of active TB actually has the disease.
*Incorrect 1.4*
- This value is not a valid probability, as probabilities must be between 0 and 1.0.
- It might arise from an incorrect calculation or misinterpretation of the provided data.
*Incorrect 0.50*
- This value does not correspond to any standard diagnostic metric calculated from the provided data.
- The actual prevalence of TB (based on positive sputum) is 1000/5200 = 0.19, not 0.50.
- This is likely a distractor with no meaningful interpretation in this context.
*Incorrect 0.70*
- This value represents the **sensitivity** of the sputum test for detecting active TB.
- Sensitivity is calculated as true positives (700) divided by total with disease (700 + 300 = 1000). So, 700 / 1000 = 0.70.
- Sensitivity tells us how good the test is at detecting disease when present, not the probability of having disease given a positive clinical diagnosis.
*Incorrect 0.88*
- This value represents the **specificity** of the clinical assessment.
- Specificity is calculated as true negatives (2100) divided by total without disease (2100 + 300 = 2400). So, 2100 / 2400 = 0.875 ≈ 0.88.
- Specificity tells us how good the assessment is at ruling out disease in those without it, not the probability of disease given a positive assessment.
Probabilistic reasoning US Medical PG Question 6: A 52-year-old man comes to the physician because of a 3-week history of a cough and hoarseness. He reports that the cough is worse when he lies down after lunch. His temperature is 37.5°C (99.5°F); the remainder of his vital signs are within normal limits. Because the physician has recently been seeing several patients with the common cold, the diagnosis of a viral upper respiratory tract infection readily comes to mind. The physician fails to consider the diagnosis of gastroesophageal reflux disease, which the patient is later found to have. Which of the following most accurately describes the cognitive bias that the physician had?
- A. Framing
- B. Anchoring
- C. Visceral
- D. Confirmation
- E. Availability (Correct Answer)
Probabilistic reasoning Explanation: ***Availability***
- The physician recently seeing several patients with the common cold led to this diagnosis readily coming to mind, demonstrating how easily recalled examples can disproportionately influence diagnosis.
- This bias occurs when easily recalled instances or information (like recent cases of common cold) are used to estimate the likelihood or frequency of an event, even if other more relevant data exist.
*Framing*
- This bias occurs when the way information is presented (e.g., as a gain or a loss) influences a decision, rather than the intrinsic characteristics of the options themselves.
- The scenario does not involve the presentation of information in different ways to sway the physician's judgment.
*Anchoring*
- This bias involves relying too heavily on an initial piece of information (the "anchor") when making subsequent judgments, often leading to insufficient adjustment away from that anchor.
- While the physician initially considered a viral URI, the setup is more about the ease of recall influencing the decision rather than being stuck on an initial data point.
*Visceral*
- This is not a commonly recognized cognitive bias in the context of medical decision-making; "visceral" largely refers to emotional or intuitive feelings rather than a structured cognitive bias.
- Cognitive biases describe systematic patterns of deviation from norm or rationality in judgment, not merely emotional responses.
*Confirmation*
- This bias involves seeking, interpreting, favoring, and recalling information in a way that confirms one's pre-existing beliefs or hypotheses.
- The physician did not actively seek information to confirm the common cold diagnosis; rather, the diagnosis came to mind due to recent encounters, which aligns with availability bias.
Probabilistic reasoning US Medical PG Question 7: A research study is comparing 2 novel tests for the diagnosis of Alzheimer’s disease (AD). The first is a serum blood test, and the second is a novel PET radiotracer that binds to beta-amyloid plaques. The researchers intend to have one group of patients with AD assessed via the novel blood test, and the other group assessed via the novel PET examination. In comparing these 2 trial subsets, the authors of the study may encounter which type of bias?
- A. Selection bias (Correct Answer)
- B. Confounding bias
- C. Recall bias
- D. Measurement bias
- E. Lead-time bias
Probabilistic reasoning Explanation: ***Selection bias***
- This occurs when different patient groups are assigned to different interventions or measurements in a way that creates **systematic differences** between comparison groups.
- In this study, having **separate patient groups** assessed with different diagnostic methods (blood test vs. PET scan) means any differences observed could be due to **differences in the patient populations** rather than differences in test performance.
- To validly compare two diagnostic tests, both tests should ideally be performed on the **same patients** (paired design) or patients should be **randomly assigned** to receive one test or the other, ensuring comparable groups.
- This is a fundamental **study design flaw** that prevents valid comparison of the two diagnostic methods.
*Measurement bias*
- Also called information bias, this occurs when there are systematic errors in how outcomes or exposures are measured.
- While using different measurement tools could introduce measurement variability, the primary issue here is that **different patient populations** are being compared, not just different measurement methods on the same population.
- Measurement bias would be more relevant if the same patients were assessed with both methods but one method was systematically misapplied or measured incorrectly.
*Confounding bias*
- This occurs when an extraneous variable is associated with both the exposure and outcome, distorting the observed relationship.
- While patient characteristics could confound results, the fundamental problem is the **study design itself** (separate groups for separate tests), which is selection bias.
*Recall bias*
- This involves systematic differences in how participants remember or report past events, common in **retrospective case-control studies**.
- Not relevant here, as this involves prospective diagnostic testing, not recollection of past exposures.
*Lead-time bias*
- Occurs in screening studies when earlier detection makes survival appear longer without changing disease outcomes.
- Not applicable to this scenario, which focuses on comparing two diagnostic methods in separate patient groups, not on survival or disease progression timing.
Probabilistic reasoning US Medical PG Question 8: A 57-year-old man presents to the clinic for a chronic cough over the past 4 months. The patient reports a productive yellow/green cough that is worse at night. He denies any significant precipitating event prior to his symptoms. He denies fever, chest pain, palpitations, weight changes, or abdominal pain, but endorses some difficulty breathing that waxes and wanes. He denies alcohol usage but endorses a 35 pack-year smoking history. A physical examination demonstrates mild wheezes, bibasilar crackles, and mild clubbing of his fingertips. A pulmonary function test is subsequently ordered, and partial results are shown below:
Tidal volume: 500 mL
Residual volume: 1700 mL
Expiratory reserve volume: 1500 mL
Inspiratory reserve volume: 3000 mL
What is the functional residual capacity of this patient?
- A. 4500 mL
- B. 2000 mL
- C. 2200 mL
- D. 3200 mL (Correct Answer)
- E. 3500 mL
Probabilistic reasoning Explanation: ***3200 mL***
- The **functional residual capacity (FRC)** is the volume of air remaining in the lungs after a normal expiration.
- It is calculated as the sum of the **expiratory reserve volume (ERV)** and the **residual volume (RV)**. In this case, 1500 mL (ERV) + 1700 mL (RV) = 3200 mL.
*4500 mL*
- This value represents the sum of the **inspiratory reserve volume (3000 mL)** and the **residual volume (1700 mL)**, which does not correspond to a standard lung volume or capacity.
- It does not logically relate to the definition of functional residual capacity.
*2000 mL*
- This value represents the sum of the **tidal volume (500 mL)** and the **expiratory reserve volume (1500 mL)**, which is incorrect for FRC.
- This would represent the inspiratory capacity minus the inspiratory reserve volume, which is not a standard measurement used in pulmonary function testing.
*2200 mL*
- This value could be obtained by incorrectly adding the **tidal volume (500 mL)** and the **residual volume (1700 mL)**, which is not the correct formula for FRC.
- This calculation represents a miscombination of lung volumes that does not correspond to any standard pulmonary capacity measurement.
*3500 mL*
- This value is the sum of the **tidal volume (500 mL)**, the **expiratory reserve volume (1500 mL)**, and the **residual volume (1700 mL)**.
- This would represent the FRC plus the tidal volume, which is not a standard measurement and does not represent the functional residual capacity.
Probabilistic reasoning US Medical PG Question 9: A medical research study is beginning to evaluate the positive predictive value of a novel blood test for non-Hodgkin’s lymphoma. The diagnostic arm contains 700 patients with NHL, of which 400 tested positive for the novel blood test. In the control arm, 700 age-matched control patients are enrolled and 0 are found positive for the novel test. What is the PPV of this test?
- A. 400 / (400 + 0) (Correct Answer)
- B. 700 / (700 + 300)
- C. 400 / (400 + 300)
- D. 700 / (700 + 0)
- E. 700 / (400 + 400)
Probabilistic reasoning Explanation: ***400 / (400 + 0) = 1.0 or 100%***
- The **positive predictive value (PPV)** is calculated as **True Positives / (True Positives + False Positives)**.
- In this scenario, **True Positives (TP)** are the 400 patients with NHL who tested positive, and **False Positives (FP)** are 0, as no control patients tested positive.
- This gives a PPV of 400/400 = **1.0 or 100%**, indicating that all patients who tested positive actually had the disease.
*700 / (700 + 300)*
- This calculation does not align with the formula for PPV based on the given data.
- The denominator `(700+300)` suggests an incorrect combination of various patient groups.
*400 / (400 + 300)*
- The denominator `(400+300)` incorrectly includes 300, which is the number of **False Negatives** (patients with NHL who tested negative), not False Positives.
- PPV focuses on the proportion of true positives among all positive tests, not all diseased individuals.
*700 / (700 + 0)*
- This calculation incorrectly uses the total number of patients with NHL (700) as the numerator, rather than the number of positive test results in that group.
- The numerator should be the **True Positives** (400), not the total number of diseased individuals.
*700 / (400 + 400)*
- This calculation uses incorrect values for both the numerator and denominator, not corresponding to the PPV formula.
- The numerator 700 represents the total number of patients with the disease, not those who tested positive, and the denominator incorrectly sums up values that don't represent the proper PPV calculation.
Probabilistic reasoning US Medical PG Question 10: A student health coordinator plans on leading a campus-wide HIV screening program that will be free for the entire undergraduate student body. The goal is to capture as many correct HIV diagnoses as possible with the fewest false positives. The coordinator consults with the hospital to see which tests are available to use for this program. Test A has a sensitivity of 0.92 and a specificity of 0.99. Test B has a sensitivity of 0.95 and a specificity of 0.96. Test C has a sensitivity of 0.98 and a specificity of 0.93. Which of the following testing schemes should the coordinator pursue?
- A. Test A on the entire student body followed by Test B on those who are positive
- B. Test A on the entire student body followed by Test C on those who are positive
- C. Test C on the entire student body followed by Test B on those who are positive
- D. Test C on the entire student body followed by Test A on those who are positive (Correct Answer)
- E. Test B on the entire student body followed by Test A on those who are positive
Probabilistic reasoning Explanation: ***Test C on the entire student body followed by Test A on those who are positive***
- To "capture as many correct HIV diagnoses as possible" (maximize true positives), the initial screening test should have the **highest sensitivity**. Test C has the highest sensitivity (0.98).
- To "capture as few false positives as possible" (maximize true negatives and confirm diagnoses), the confirmatory test should have the **highest specificity**. Test A has the highest specificity (0.99).
*Test A on the entire student body followed by Test B on those who are positive*
- Starting with Test A (sensitivity 0.92) would miss more true positive cases than starting with Test C (sensitivity 0.98), failing the goal of **capturing as many cases as possible**.
- Following with Test B (specificity 0.96) would result in more false positives than following with Test A (specificity 0.99).
*Test A on the entire student body followed by Test C on those who are positive*
- This scheme would miss many true positive cases initially due to Test A's lower sensitivity compared to Test C.
- Following with Test C would introduce more false positives than necessary, as it has a lower specificity (0.93) than Test A (0.99).
*Test C on the entire student body followed by Test B on those who are positive*
- While Test C is a good initial screen for its high sensitivity, following it with Test B (specificity 0.96) is less optimal than Test A (specificity 0.99) for minimizing false positives in the confirmation step.
- This combination would therefore yield more false positives in the confirmatory stage than using Test A.
*Test B on the entire student body followed by Test A on those who are positive*
- Test B has a sensitivity of 0.95, which is lower than Test C's sensitivity of 0.98, meaning it would miss more true positive cases at the initial screening stage.
- While Test A provides excellent specificity for confirmation, the initial screening step is suboptimal for the goal of capturing as many diagnoses as possible.
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