sandy wrote:
The probabilities that each of two independent experiments will have a successful outcome are \(\frac{8}{15}\) and \(\frac{2}{3}\), respectively. What is the probability that both experiments will have successful outcomes?
A. \(\frac{4}{5}\)
B. \(\frac{6}{5}\)
C. \(\frac{2}{15}\)
D. \(\frac{16}{45}\)
E. \(\frac{64}{225}\)
We know
when A and B are two independent experiments then,
Probability of (A) and Probability of (B) = Probability of (A) * Probability of (B)
Here Probability of (A) =\(\frac{8}{15}\)
Probability of (B) = \(\frac{2}{3}\)
Therefore the probability that both experiments will have successful outcomes = \(\frac{8}{15} * \frac{2}{3}\) = \(\frac{16}{45}\)