M7MBA wrote: ↑

Sun Sep 19, 2021 11:42 am

On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

Answer: B

Source: Official Guide

NOTE: if P(rain on a certain day) = 0.2, then we know that P(NO rain on a certain day) = 1 - 0.2 = 0.8

For probability questions, I always ask, "What needs to happen for the desired event to occur?"

For this question P(come home Monday night) = P(no rain on Saturday AND no rain on Sunday AND rain on Monday)

At this point, we can apply what we know about AND probabilities. We get:
P(come home Monday night) = P(no rain on Saturday) X P(no rain on Sunday) X P(rain on Monday)
= (0.8) X (0.8) X (0.2)
= 0.128

Answer: B