Two friends, Ronak and Sohan, appear in an interview. The probability that Ronak is selected is 40% and the probability that Sohan is selected is \(66\frac{2}{3}\)%. If the two selections are independent, what is the probability that neither of them is selected?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20%
The probability that an event does not happen is \(1-\) the probability that it happens. For independent events, “neither selected” is the product of the two “not selected” probabilities.
P(Ronak selected) \(\displaystyle =40\%=\frac{2}{5}\), so P(Ronak not selected) \(\displaystyle =\frac{3}{5}\)
P(Sohan selected) \(\displaystyle =66\frac{2}{3}\%=\frac{2}{3}\), so P(Sohan not selected) \(\displaystyle =\frac{1}{3}\)
P(neither selected) \(\displaystyle =\frac{3}{5}\times\frac{1}{3}=\frac{1}{5}=20\%\)