If the probability that A will survive the next 15 years is 7/8, and the…
2023
If the probability that A will survive the next 15 years is 7/8, and the probability that B will survive the next 15 years is 9/10, and the two events are independent, what is the probability that both A and B will survive the next 15 years?
- A.
1/20
- B.
63/80
- C.
1/5
- D.
None of these
Attempted by 72 students.
Show answer & explanation
Correct answer: B
Concept: For two independent events, the probability that both occur is the product of their individual probabilities: P(A and B) = P(A) × P(B). This multiplication rule holds whenever one event's outcome does not affect the other's probability.
Application:
The probability that A survives the next 15 years is P(A) = 7/8, and the probability that B survives the next 15 years is P(B) = 9/10.
Since A's and B's survival are independent events, P(both survive) = P(A) × P(B) = 7/8 × 9/10.
Multiply the numerators (7 × 9 = 63) and the denominators (8 × 10 = 80): P(both survive) = 63/80.
Cross-check: 63/80 = 0.7875, which is smaller than each individual probability (7/8 = 0.875 and 9/10 = 0.9) — exactly as expected, since the joint probability of two independent events must be less than or equal to the smaller of the two individual probabilities.
Answer: 63/80