Page 261 - Probability Demystified

APPENDIX 251

EXAMPLE: Two video products distributors supply video tape boxes to
a video production company. Company A sold 100 boxes of which 5 were
defective. Company B sold 300 boxes of which 21 were defective. If a box
was defective, find the probability that it came from Company B.

SOLUTION:
Let P(A) ¼ probability that a box selected at random is from company A.
1
3
Then, PðAÞ¼ 100 ¼ ¼ 0:25; PðBÞ¼ PðAÞ¼ 300 ¼ ¼ 0:75. Since there are 5
400 4 400 4
defective boxes from Company A, PðDjAÞ¼ 5 ¼ 0:05 and there are 21
100
defective boxes from Company B or A,so PðDjAÞ¼ 21 ¼ 0:07 . The prob-
300
abilities are shown in Figure A-2.

Fig. A-2.

PðAÞ PðDjAÞ
PðAjDÞ¼
PðAÞ PðDjAÞþ PðAÞ PðDjAÞ

ð0:25Þð0:05Þ
¼
ð0:25Þð0:05Þþð0:75Þð0:07Þ

0:0125 0:0125
¼ ¼ ¼ 0:192
0:0125 þ 0:0525 0:065

PRACTICE

1. Box I contains 6 green marbles and 4 yellow marbles. Box II contains
5 yellow marbles and 5 green marbles. A box is selected at random
and a marble is selected from the box. If the marble is green, find the
probability it came from Box I.
2. An auto parts store purchases rebuilt alternators from two suppliers.
From Supplier A, 150 alternators are purchased and 2% are defective.
From Supplier B, 250 alternators are purchased and 3% are defective.