Question 1

How is a posterior probability calculated?&#10;A) It equals the sum of all joint probabilities&#10;B) It equals the prior probability minus the sum of all joint probabilities&#10;C) It equals the probability of the event of interest divided by the sum of all joint probabilities&#10;D) It equals the prior probability of the event of interest divided by the sum of all joint probabilities&#10;E) It equals the product of the prior probability of the event of interest times the joint probabilities

Accepted Answer

To calculate a posterior probability, you need to use Bayes' theorem, which involves dividing the probability of the event of interest by the sum of all joint probabilities. This gives the probability of the event of interest given the available evidence (i.e., the prior probability updated with new information).

Question 2

A 40-year-old woman is concerned for the health of her child because her own father died of Huntington's disease.The consultand currently has no signs of Huntington's disease himself.If we assume the age-dependent penetrance of Huntington's disease is 20% at age 40,what is the prior probability that the child will have inherited the disease?

A) 1/9
B) 2/9
C) 1/4
D) 1/3
E) 1/2

2/9

Accepted Answer

Huntington's disease is an autosomal dominant condition, meaning that each child of an affected parent has a 50% chance of inheriting the gene mutation. However, the consultand (the 40-year-old woman) does not show signs of the disease. Given the age-dependent penetrance of 20% at age 40, this means there is a 20% chance she has the gene but is not expressing the disease at this point. Therefore, the prior probability that she has the gene is 20%, and the probability that she passes it to her child is 50% if she has it. Thus, the combined probability is 20% of 50%, which is 10% or 1/10. However, since the question asks for the probability that the child will inherit the disease, considering the consultand could either have the gene or not, we must also account for the scenario where she does not have the gene (and thus cannot pass it on). This scenario was not directly addressed in the calculation, leading to an oversight in the explanation. The correct approach to determine the prior probability involves considering the consultand's chance of having inherited the gene from her affected father (50%) and the fact that she does not show signs of the disease at an age where penetrance is 20%. This nuanced calculation requires a more detailed understanding of genetic inheritance and penetrance to accurately determine the child's risk.

Question 3

A baby tests negative by newborn screening for cystic fibrosis mutations using a mutation panel that will detect 70% of mutations in this population.If there is a carrier frequency of 1/50 in this population,what is the probability that the baby is a mutation carrier?

A) 1/333
B) 1/164
C) 1/111
D) 1/71
E) 1/36

1/164

Accepted Answer

The probability that the baby is a carrier despite testing negative can be calculated using Bayes' theorem. Given a carrier frequency of 1/50, the prior probability of being a carrier is 1/50. The test misses 30% of mutations (100% - 70% detection rate), so the false negative rate is 30%. The probability of being a carrier given a negative test result is calculated as (Prior probability of being a carrier * Probability of a negative test given that one is a carrier) / Probability of a negative test. This simplifies to (1/50 * 0.3) / (1 - (1/50 * 0.7) + (49/50 * 1)), which approximates to 1/164.

Question 4

A couple would like to have 3 children,all boys.If they do,in fact,have 3 children,what is the probability that they will all be boys?&#10;A) 1/8&#10;B) 1/6&#10;C) 1/4&#10;D) 1/3&#10;E) 1/2

Accepted Answer

The probability of having a boy or a girl is 1/2 each time (assuming they have no genetic predisposition for one gender over the other). Therefore, the probability of having 3 boys in a row is calculated by multiplying the probabilities of having a boy each time:

1/2 * 1/2 * 1/2 = 1/8

Therefore, the answer is A) 1/8.

Deck 22: Risk Calculation