Consider n independent trials of an experiment in which each

Consider n independent trials of an experiment in which each trial has two possible outcomes: \"success\" or \"failure.\" The probability of a success on each trial is p, and the probability of a failure is q = 1 - p. In this context, the term n^CkP^kq^n-k in the expansion of (p + q)^n gives the probability of k successes in the n trials of the experiment. The probability of a baseball player getting a hit during any given time at bat is 1/4. To find the probability that the player gets two hits during the next 9 times at bat, evaluate the term shown below in the expansion of (1/4 + 3/4)^9. (Round your answer to four decimal places.) 9C2(1/4^2 (3/4)^7

Solution

9C2 = 9! / 2! (9-2)! = 36

36 * (1/4)^2 * (3/4)^7 = 0.3003