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Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8. If all hit at the target independently, then the probability that the target would be hit is
- a)25/192
- b)1/192
- c)25/32
- d)7/32
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Four persons can hit a target correctly with probabilities 1/2, 1/3, 1...
Let person be A, B, C, D.
P(Hit) = 1 - P(None of them hits)
P(Hit) = 1 - P(None of them hits)
Most Upvoted Answer
Four persons can hit a target correctly with probabilities 1/2, 1/3, 1...
Probability of hitting the target by each person:
- Person 1: 1/2
- Person 2: 1/3
- Person 3: 1/4
- Person 4: 1/8
Probability of not hitting the target by each person:
- Person 1: 1 - 1/2 = 1/2
- Person 2: 1 - 1/3 = 2/3
- Person 3: 1 - 1/4 = 3/4
- Person 4: 1 - 1/8 = 7/8
Probability of all four persons hitting the target:
- This can be calculated by multiplying the probabilities of hitting the target for each person.
- (1/2) * (1/3) * (1/4) * (1/8) = 1/192
Probability of at least one person hitting the target:
- This can be calculated by finding the complement of the probability that none of them hit the target.
- Probability that none of them hit the target = (1/2) * (2/3) * (3/4) * (7/8) = 7/32
- Probability that at least one person hits the target = 1 - 7/32 = 25/32
Therefore, the probability that the target would be hit when all four persons hit independently is 25/32.
- Person 1: 1/2
- Person 2: 1/3
- Person 3: 1/4
- Person 4: 1/8
Probability of not hitting the target by each person:
- Person 1: 1 - 1/2 = 1/2
- Person 2: 1 - 1/3 = 2/3
- Person 3: 1 - 1/4 = 3/4
- Person 4: 1 - 1/8 = 7/8
Probability of all four persons hitting the target:
- This can be calculated by multiplying the probabilities of hitting the target for each person.
- (1/2) * (1/3) * (1/4) * (1/8) = 1/192
Probability of at least one person hitting the target:
- This can be calculated by finding the complement of the probability that none of them hit the target.
- Probability that none of them hit the target = (1/2) * (2/3) * (3/4) * (7/8) = 7/32
- Probability that at least one person hits the target = 1 - 7/32 = 25/32
Therefore, the probability that the target would be hit when all four persons hit independently is 25/32.
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Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8.If all hit at the target independently, then the probability that the target would be hit isa)25/192b)1/192c)25/32d)7/32Correct answer is option 'C'. Can you explain this answer?
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