1 On each of three consecutive days the National Weather Ser

1. On each of three consecutive days the National Weather Service announces that there is a 50-50 chance of rain. Assuming that the National Weather Service is correct, what is the probability that it rains on at most one of the three days? Justify your answer. (Hint: Represent the outcome that it rains on day 1 and doesn\'t rain on days 2 and 3 as RNN.)

Solution

The Maximum possible outcomes : {NNN, RNN, NRN, NNR, RRN, RNR, NRR, RRR}

Then total outcomes = 8

And outcomes at most rain on one of three days = NNN, RNN, NRN, NNR = 4

Then the probability of at most rain on one of three days is 4/8 = 1/2