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Two men hit at a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?
- a)1/2
- b)1/3
- c)1/6
- d)2/3
Correct answer is option 'A'. Can you explain this answer?
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Problem:
Two men hit at a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?
Solution:
To find the probability that exactly one of the two men hits the target, we need to consider two scenarios:
1. The first man hits the target, while the second man misses.
2. The first man misses the target, while the second man hits.
Scenario 1:
The probability of the first man hitting the target is 1/2. The probability of the second man missing the target is 1 - 1/3 = 2/3. Therefore, the probability of scenario 1 occurring is (1/2) * (2/3) = 1/3.
Scenario 2:
The probability of the first man missing the target is 1 - 1/2 = 1/2. The probability of the second man hitting the target is 1/3. Therefore, the probability of scenario 2 occurring is (1/2) * (1/3) = 1/6.
Final Probability:
To find the probability that exactly one of the two men hits the target, we need to add the probabilities of the two scenarios:
P(exactly one hits) = P(scenario 1) + P(scenario 2) = 1/3 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3.
Therefore, the correct answer is option 'A' (1/2).
Two men hit at a target with probabilities 1/2 and 1/3 respectively. What is the probability that exactly one of them hits the target?
Solution:
To find the probability that exactly one of the two men hits the target, we need to consider two scenarios:
1. The first man hits the target, while the second man misses.
2. The first man misses the target, while the second man hits.
Scenario 1:
The probability of the first man hitting the target is 1/2. The probability of the second man missing the target is 1 - 1/3 = 2/3. Therefore, the probability of scenario 1 occurring is (1/2) * (2/3) = 1/3.
Scenario 2:
The probability of the first man missing the target is 1 - 1/2 = 1/2. The probability of the second man hitting the target is 1/3. Therefore, the probability of scenario 2 occurring is (1/2) * (1/3) = 1/6.
Final Probability:
To find the probability that exactly one of the two men hits the target, we need to add the probabilities of the two scenarios:
P(exactly one hits) = P(scenario 1) + P(scenario 2) = 1/3 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3.
Therefore, the correct answer is option 'A' (1/2).
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