A brother and sister appear for an interview against two vacant posts in an…
2025
A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother's selection is 1/5th and that of the sister's selections is 1/3rd. What is the probability that one of them is selected?
- A.
⅕
- B.
⅖
- C.
⅓
- D.
⅔
Attempted by 40 students.
Show answer & explanation
Correct answer: B
Answer: 2/5
Let B be the event the brother is selected (P(B)=1/5) and S be the event the sister is selected (P(S)=1/3). Assume selections are independent.
Probability only the brother is selected = P(B) * (1 - P(S)) = (1/5) * (2/3) = 2/15.
Probability only the sister is selected = P(S) * (1 - P(B)) = (1/3) * (4/5) = 4/15.
Total probability exactly one is selected = 2/15 + 4/15 = 6/15 = 2/5.
Note: If asked for the probability that at least one is selected, compute 1 - P(neither) = 1 - (4/5)*(2/3) = 7/15, which is different from the required answer.