The probability that A hits a target is 1/4, and the probability that B hits…
2025
The probability that A hits a target is 1/4, and the probability that B hits the target is 2/5. Both shoot at the target independently. What is the probability that at least one of them hits the target, i.e., that A or B (or both) hit the target?
- A.
3/5
- B.
11/9
- C.
2/20
- D.
11/20
Attempted by 118 students.
Show answer & explanation
Correct answer: D
Concept: For two independent events A and B, the probability that at least one occurs is best found using the complement rule: P(at least one) = 1 minus P(neither occurs). Since A and B shoot independently (as stated), P(neither occurs) = P(A does not occur) times P(B does not occur).
Application: Apply this to the given probabilities, P(A hits) = 1/4 and P(B hits) = 2/5.
Probability A does not hit = 1 minus 1/4 = 3/4.
Probability B does not hit = 1 minus 2/5 = 3/5.
Since the two shots are independent, probability neither hits = 3/4 times 3/5 = 9/20.
Probability at least one hits = 1 minus 9/20 = 11/20.
Cross-check: This can also be verified with the inclusion-exclusion rule, P(A or B) = P(A) + P(B) minus P(A and B). Here P(A and B) = 1/4 times 2/5 = 1/10 (the probability both hit, given independence), so P(A or B) = 1/4 + 2/5 minus 1/10 = 5/20 + 8/20 minus 2/20 = 11/20 -- the same value, confirming the result.
So the probability that at least one of them hits the target is 11/20.
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