Suppose that you and wo friends go to a restaurant and reque

Suppose that you and wo friends go to a restaurant and request to be served bu the most popular waiter there, who filled 91.2% of his orders correctly last month.

a.) Before you find the probability, define the random variable and establish its distribution. Justify your answer.

b.) What is the probability that exactly two of the orders will be filled correctly?

Solution

a)

The random variable x is the number of correctly filled orders out of n = 3 trials.

The distribution is binomial, because there are only 2 possible results, and each trial are independent. Furthermore, the probability of a success is constant at 0.912, and the number of trials is fixed.

b)

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 =    0.912      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.219580416 [ANSWER]