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

Event A: replies 3/10 messages

Event B: sits by the pool 4/7 days per week

When we say independent events, the next events are not affected by the previous events.

The probability of Event A and B is equal to the probability of A multiplied to the Probability of B. In this case, we have:

`P(A)* P(B)=(3)/(10)*(4)/(7)=(12)/(70)=(6)/(35)_{}`

Thus, the probability that she replies to a text and sits by the pool is 6/35 or 17.14%.