Consider a binomial experiment made up of three trials with outcomes of success, S, and failure, F, where P(S) p and P(F) q.

a. Complete the accompanying tree diagram. Label all branches completely.

b. In column

(b) of the tree diagram, express the probability of each outcome represented by the branches as a product of powers of p and q.

c. Let x be the random variable, the number of successes observed. In column (c), identify the value of x for each branch of the tree diagram.

d. Notice that all the products in column

(b) are made up of three factors and that the value of the random variable is the same as the exponent for the number p.

e. Write the equation for the binomial probability function for this situation.

Start Trial Trial Trial (b) (c) 1 2 3 Probability x S p3 3 S F pq 2 S F F