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John and Dani go for an interview for two vacancies. The probability for the selection of John is 1/3 and whereas the probability for the selection of Dani is 1/5. What is the probability that only one of them is selected?
- a)3/5
- b)2/5
- c)1/5
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
John and Dani go for an interview for two vacancies. The probability f...
Let A = the event that John is selected and B = the event that Dani is selected.
Given that 𝑃(𝐴) = 1/3 and 𝑃(𝐵) = 1/5
We know that A is the event that A does not occur and B is the event that B does not occur
Probability that only one of them is selected
Most Upvoted Answer
John and Dani go for an interview for two vacancies. The probability f...
Solution:
To find the probability that only one of them is selected, we need to add the probabilities of John being selected and Dani not being selected, and the probabilities of Dani being selected and John not being selected.
P(John selected and Dani not selected) = P(John) * (1 - P(Dani)) = 1/3 * (1 - 1/5) = 2/15
P(Dani selected and John not selected) = P(Dani) * (1 - P(John)) = 1/5 * (1 - 1/3) = 2/15
Adding these probabilities, we get:
P(only one of them selected) = 2/15 + 2/15 = 4/15
Therefore, the correct answer is option B) 2/5.
To find the probability that only one of them is selected, we need to add the probabilities of John being selected and Dani not being selected, and the probabilities of Dani being selected and John not being selected.
P(John selected and Dani not selected) = P(John) * (1 - P(Dani)) = 1/3 * (1 - 1/5) = 2/15
P(Dani selected and John not selected) = P(Dani) * (1 - P(John)) = 1/5 * (1 - 1/3) = 2/15
Adding these probabilities, we get:
P(only one of them selected) = 2/15 + 2/15 = 4/15
Therefore, the correct answer is option B) 2/5.
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