Page 131 - Probability Demystified

120 CHAPTER 7 The Binomial Distribution

Note: Most statistics books have tables that can be used to compute
probabilities for binomial variables.

PRACTICE

1. A student takes a 5-question true–false quiz. Since the student has not
studied, he decides to flip a coin to determine the answers. What is the
probability that the student guesses exactly 3 out of 5 correctly?
2. A basketball player makes three-fourths of his free throws. Assume
each shot is independent of another shot. Find the probability that he
makes the next four free throws.
3. A circuit has 6 breakers. The probability that each breaker will fail is
0.1. If the circuit is activated, find the probability that exactly two
breakers will fail. Each breaker is independent of any other breaker.
4. Eight coins are tossed; find the probability of getting exactly 3 heads.
5. A box contains 4 red marbles and 2 white marbles. A marble is drawn
and replaced four times. Find the probability of getting exactly 3 red
marbles and one white marble.

ANSWERS
1
1. n ¼ 5, x ¼ 3, p ¼
2
1 3 1 2
P(exactly 3 correct) ¼ C 3
5
2 2
1
¼ð10Þ
32
5
¼ ¼ 0:3125
16
3
2. n ¼ 4, x ¼ 4, p ¼
4
3 4 1 0
Pð4 successesÞ¼ C 4
4
4 4
81
¼ 0:3164
256
3. n ¼ 6, x ¼ 2, p ¼ (0.1)
2 4
Pð2 will failÞ¼ C ð0:1Þ ð0:9Þ
6
2
¼ 15ð0:006561Þ¼ 0:098415