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 nCk pkqn-k in the expansion of (p + q)n gives the probability of k successes in the n trials of the experiment.
1. You toss a fair coin seven times. To find the probability of obtaining four heads, evaluate the term
7C4 (1/2)4 (1/2)3
in the expansion of (1/2 + ½)7.
2. The probability of a baseball player getting a hit during any given time at bat is 14 . To find the probability that the player gets three hits during the next 10 times at bat, evaluate the term
10C3 (1/4)3 (3/5)7
in the expansion of (1/4 + 3/4)10.
3. The probability of a sales representative making a sale with any one customer is 13. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term
8C4 (1/3)4 (2/3)4
in the expansion of (1/3 + 2/3)8.
4. To find the probability that the sales representative in Exercise 79 makes four sales when the probability of a sale with any one customer is 1/2, evaluate the term
8C4 (1/2)4 (1/2)4
in the expansion of (1/2 + 1/2)8.