Answer to Question #261806 in Statistics and Probability for cam

Question

Jane randomly replies to three out of every ten messages she receives. She also chooses to sit by the pool four out of seven days each week. Assuming replying to texts and sitting by the pool are independent events, what is the probability that she replies to a text and sits by the pool? Give your answer as an exact fraction and reduce the fraction as much as possible.

Answer 1

Assuming replying to texts and sitting by the pool are independent events

$$P(replies\ and \ sits)=P(replies)P(sits)$$

$$=\dfrac{3}{10}\big(\dfrac{4}{7}\big)=\dfrac{6}{35}$$