Society of Actuaries Probability (P) Practice Test
Exam
1. A survey of 100 students found that 40 play tennis, 30 play
golf, and 10 play both. What is the probability that a randomly
selected student plays neither?
A) 0.20
B) 0.30
C) 0.40
D) 0.50
E) 0.60
Correct Answer: C
Rationale: Using the addition rule, P(T ∪ G) = 0.40 + 0.30 − 0.10
= 0.60. The probability of neither is 1 − 0.60 = 0.40 .
2. If P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.2, what is P(A | B)?
A) 0.2
,B) 0.3
C) 0.4
D) 0.5
E) 0.8
Correct Answer: D
Rationale: By definition, P(A | B) = P(A ∩ B) / P(B) = 0..4 =
0.5.
3. A box contains 5 red balls and 3 blue balls. Two balls are
drawn without replacement. What is the probability both are
red?
A) 5/28
B) 5/14
C) 25/64
D) 3/14
E) 2/7
Correct Answer: B
,Rationale: P(R₁) = 5/8. After drawing one red, P(R₂ | R₁) = 4/7.
The joint probability is (5/8) × (4/7) = 20/56 = 5/14.
4. If events A and B are mutually exclusive with P(A) = 0.3 and
P(B) = 0.4, what is P(A ∪ B)?
A) 0.12
B) 0.58
C) 0.70
D) 0.80
E) 1.00
Correct Answer: C
Rationale: For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪
B) = P(A) + P(B) = 0.3 + 0.4 = 0.7.
5. A test for a disease has a sensitivity of 95% and a specificity
of 90%. The disease prevalence is 1%. What is the probability
that a person who tests positive actually has the disease?
, A) 0.088
B) 0.095
C) 0.105
D) 0.150
E) 0.200
Correct Answer: A
Rationale: Using Bayes' theorem: P(D | +) = (0.95 × 0.01) /
[(0.95 × 0.01) + (0.10 × 0.99)] = 0..1085 ≈ 0.0876.
6. How many ways can 3 people be selected from a group of 8
to form a committee?
A) 24
B) 56
C) 112
D) 336
E) 512
Correct Answer: B
Exam
1. A survey of 100 students found that 40 play tennis, 30 play
golf, and 10 play both. What is the probability that a randomly
selected student plays neither?
A) 0.20
B) 0.30
C) 0.40
D) 0.50
E) 0.60
Correct Answer: C
Rationale: Using the addition rule, P(T ∪ G) = 0.40 + 0.30 − 0.10
= 0.60. The probability of neither is 1 − 0.60 = 0.40 .
2. If P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.2, what is P(A | B)?
A) 0.2
,B) 0.3
C) 0.4
D) 0.5
E) 0.8
Correct Answer: D
Rationale: By definition, P(A | B) = P(A ∩ B) / P(B) = 0..4 =
0.5.
3. A box contains 5 red balls and 3 blue balls. Two balls are
drawn without replacement. What is the probability both are
red?
A) 5/28
B) 5/14
C) 25/64
D) 3/14
E) 2/7
Correct Answer: B
,Rationale: P(R₁) = 5/8. After drawing one red, P(R₂ | R₁) = 4/7.
The joint probability is (5/8) × (4/7) = 20/56 = 5/14.
4. If events A and B are mutually exclusive with P(A) = 0.3 and
P(B) = 0.4, what is P(A ∪ B)?
A) 0.12
B) 0.58
C) 0.70
D) 0.80
E) 1.00
Correct Answer: C
Rationale: For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪
B) = P(A) + P(B) = 0.3 + 0.4 = 0.7.
5. A test for a disease has a sensitivity of 95% and a specificity
of 90%. The disease prevalence is 1%. What is the probability
that a person who tests positive actually has the disease?
, A) 0.088
B) 0.095
C) 0.105
D) 0.150
E) 0.200
Correct Answer: A
Rationale: Using Bayes' theorem: P(D | +) = (0.95 × 0.01) /
[(0.95 × 0.01) + (0.10 × 0.99)] = 0..1085 ≈ 0.0876.
6. How many ways can 3 people be selected from a group of 8
to form a committee?
A) 24
B) 56
C) 112
D) 336
E) 512
Correct Answer: B
