On each of three consecutive days the National Weather Servi

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? (Hint: Represent the outcome that it rains on day 1 and doesn’t rain on days 2 and 3 as RNN.)

Solution

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    3      
p = the probability of a success =    0.5      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.125

Thus, P(at least one) = 1 - P(0) =   0.875   [ANSWER]