A man can hit the target once in four shots. If he fires 4 shots in…
2023
A man can hit the target once in four shots. If he fires 4 shots in succession, what is the probability that he will hit the target?
- A.
1
- B.
175/256
- C.
12/16
- D.
81/256
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept: For ‘at least one success’ among independent repeated trials, use the complement rule — P(at least one hit) = 1 minus P(no hit in any trial), since ‘at least one hit’ and ‘zero hits’ are complementary events that together cover the entire probability space.
The probability of hitting the target in a single shot is 1/4, so the probability of missing it in a single shot is 1 minus 1/4 = 3/4.
Since the 4 shots fired in succession are independent trials, the probability of missing all 4 shots is (3/4)4 = 81/256.
By the complement rule, the probability of hitting the target at least once is 1 minus 81/256 = 175/256.
Cross-check: the probability of missing all shots (81/256) and the probability of hitting at least once (175/256) must together account for every outcome: 81/256 + 175/256 = 256/256 = 1, confirming the result.
