Question

Brother and Sister both appear for an interview. The probability of the selection of brother is \(\frac{1}{8}\) while the probability of rejection of sister is \(\frac{4}{5}\). What is the probability that only one of them is selected?

• A. \(\frac{11}{40}\)
• B. \(\frac{5}{13}\)
• C. \(\frac{1}{10}\)
• D. \(\frac{7}{40}\)

Answer 1

The Correct Option is A

To solve this problem, we need to find the probability that only one out of the brother or sister gets selected. This involves a basic understanding of probability, specifically independent events.

We are given: 

• The probability of the brother being selected is \(\frac{1}{8}\).
• The probability of the sister being rejected is \(\frac{4}{5}\).

The probability that the sister is selected is:

\(P(\text{sister is selected}) = 1 - P(\text{sister is rejected}) = 1 - \frac{4}{5} = \frac{1}{5}\)

To find the probability that only one of them gets selected, we consider the two mutually exclusive events:

1. Brother is selected, and sister is not selected.
2. Sister is selected, and brother is not selected.

Let's calculate these probabilities:

• Probability that brother is selected and sister is not selected:
• Probability that sister is selected and brother is not selected:

Therefore, the probability that only one of them is selected is:

\(\frac{1}{10} + \frac{7}{40} = \frac{4}{40} + \frac{7}{40} = \frac{11}{40}\)

Thus, the correct answer is:

\(\frac{11}{40}\)