Q. If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability of a true positive result if the prevalence of the disease is 1%? (2022)
Q. If a test for a disease has a sensitivity of 90% and a specificity of 95%, what is the probability that a person who tests positive actually has the disease, given that the prevalence is 1%? (2022)
Q. If a trait is controlled by a single gene with two alleles, where A is dominant over a, what is the expected phenotypic ratio in the offspring of a cross between Aa and aa?
A.
1:1
B.
3:1
C.
2:1
D.
1:2
Solution
The cross Aa x aa will produce offspring in a 1:1 phenotypic ratio (A:a).
Q. If a trait is sex-linked and recessive, what is the probability that a son will express the trait if his mother is a carrier and his father does not have the trait?
A.
0%
B.
25%
C.
50%
D.
100%
Solution
The son will inherit the X chromosome from his mother. If she is a carrier (X^HX^h), there is a 50% chance he will inherit the X^h and express the trait.
Q. If a treatment is effective in 80% of cases, what is the probability that it will be effective for at least one out of three patients? (2023)
A.
0.512
B.
0.8
C.
0.2
D.
0.64
Solution
Probability that treatment is not effective for one patient = 1 - 0.8 = 0.2. For three patients, the probability that it is not effective for all = 0.2^3 = 0.008. Therefore, the probability that it is effective for at least one = 1 - 0.008 = 0.992.
Q. If a triangle has two sides of lengths 6 and 8, what is the maximum possible length of the third side?
A.
12
B.
10
C.
14
D.
15
Solution
The maximum length of the third side is less than the sum of the other two sides, so it can be at most 6 + 8 - 1 = 13, but must also be greater than the difference, so it can be at most 10.
Q. If a vaccine reduces the risk of infection by 75%, what is the probability of infection after vaccination if the initial probability of infection is 0.2? (2020)
A.
0.05
B.
0.1
C.
0.15
D.
0.2
Solution
The probability of infection after vaccination = Initial probability × (1 - reduction) = 0.2 × (1 - 0.75) = 0.2 × 0.25 = 0.05.
Q. If a vaccine reduces the risk of infection by 75%, what is the probability of infection after vaccination if the initial probability of infection is 0.1? (2020)
A.
0.025
B.
0.075
C.
0.1
D.
0.5
Solution
The new probability of infection after vaccination = Initial probability × (1 - reduction) = 0.1 × (1 - 0.75) = 0.1 × 0.25 = 0.025.
