Page 262 - Probability Demystified
P. 262
252 APPENDIX
Given that an alternator is defective, find the probability that it came
from Supplier B.
3. Two manufacturers supply paper cups to a catering service. Manu-
facturer A supplied 100 packages and 5 were damaged. Manufacturer B
supplied 50 packages and 3 were damaged. If a package is damaged,
find the probability that it came from Manufacturer A.
4. Box 1 contains 10 balls; 7 are marked ‘‘win’’ and 3 are marked ‘‘lose.’’
Box 2 contains 10 balls; 3 are marked ‘‘win’’ and 7 are marked ‘‘lose.’’
You roll a die. If you get a 1 or 2, you select Box 1 and draw a ball.
If you roll 3, 4, 5, or 6, you select Box 2 and draw a ball. Find the
probability that Box 2 was selected if you have selected a ‘‘win.’’
5. Using the information in Exercise 4, find the probability that Box 1
was selected if a ‘‘lose’’ was drawn.
ANSWERS
1 6 3 1 5 1
1. PðB1Þ¼ ; pðGjB1Þ¼ ¼ ; PðB2Þ¼ ; PðGjB2Þ¼ ¼
2 10 5 2 10 2
PðB1Þ PðGjB1Þ
PðB1jGÞ¼
PðB1Þ PðGjB1Þþ PðB2Þ PðGjB2Þ
1 3 3
2 5 10 6
¼ ¼ ¼
1 3 1 1 3 1 11
þ þ
2 5 2 2 10 4
150 250
2. PðAÞ¼ ¼ 0:375; PðDjAÞ¼ 0:02; PðBÞ¼ ¼ 0:625
400 400
PðDjBÞ¼ 0:03
PðBÞ PðDjBÞ
PðBjDÞ¼
PðBÞ PðDjBÞþ PðAÞ PðDjAÞ
ð0:625Þð0:03Þ
¼ ¼ 0:714
ð0:625Þð0:03Þþ ð0:375Þð0:02Þ