Neha and Arjun each apply for a library card. The probability that Neha's application is accepted is \(\frac{4}{5}\) and the probability that Arjun's is accepted is \(\frac{3}{8}\). If the two decisions are independent, what is the probability that both applications are accepted?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{3}{10}\)
For independent events, the probability that both happen is the product of their probabilities.
P(Neha accepted) \(\displaystyle =\frac{4}{5}\), P(Arjun accepted) \(\displaystyle =\frac{3}{8}\)
P(both accepted) \(\displaystyle =\frac{4}{5}\times\frac{3}{8}=\frac{12}{40}=\frac{3}{10}\)