Page 146 - Probability Demystified

P. 146

CHAPTER 8 Other Probability Distributions 135

The probability is
C C
6 2 4 2
C
10 4
6! 4!

2!4! 2!2!
¼
10!
4!6!
15 6
¼
210
90 3
¼ ¼ 0:429
210 7

EXAMPLE: A lot of 12 oxygen tanks contains 3 defective ones. If 4 tanks
are randomly selected and tested, ﬁnd the probability that exactly one will
be defective.

SOLUTION:
Since there are 3 defective tanks and 9 good tanks, a ¼ 3 and b ¼ 9. If 4 tanks
are randomly selected and we want to know the probability that exactly one
is defective, n ¼ 4, x ¼ 1, and n x ¼ 4 1 ¼ 3. The probability then is
3! 9!
C C 3 84
3 1 9 3 1!2! 3!6!
¼ ¼ 0:509
C 12! 495
12 4
4!8!
PRACTICE

1. In a box of 12 shirts there are 5 defective ones. If 5 shirts are sold at
random, ﬁnd the probability that exactly two are defective.
2. In a ﬁtness club of 18 members, 10 prefer the exercise bicycle and
8 prefer the aerobic stepper. If 6 members are selected at random, ﬁnd
the probability that exactly 3 use the bicycle.
3. In a shipment of 10 lawn chairs, 6 are brown and 4 are blue. If
3 chairs are sold at random, ﬁnd the probability that all are brown.
4. A class consists of 5 women and 4 men. If a committee of 3 people is
selected at random, ﬁnd the probability that all 3 are women.
5. A box contains 3 red balls and 3 white balls. If two balls are selected
at random, ﬁnd the probability that both are red.

141 142 143 144 145 146 147 148 149 150 151