Page 74 - Probability Demystified

CHAPTER 4 The Multiplication Rules 63

EXAMPLE: Two cards are drawn without replacement from a deck of
52 cards. Find the probability that both are queens.

SOLUTION:

PðQ and QÞ¼ PðQÞ PðQjQÞ
4 3
¼
52 51
1
¼
221

This multiplication rule can be extended to include three or more events, as
shown in the next example.

EXAMPLE: A box contains 3 orange balls, 3 yellow balls, and 2 white balls.
Three balls are selected without replacement. Find the probability of
selecting 2 yellow balls and a white ball.

SOLUTION:
3 2 2
Pðyellow and yellow and whiteÞ¼
8 7 6
3 1 2 1 2 1
¼
8 4 7 6 1
1
¼
28
Remember that the key word for the multiplication rule is and. It means to
multiply.
When two events are dependent, the probability that the second event
occurs must be adjusted for the occurrence of the first event. For the
mathematical purist, only one multiplication rule is necessary for two events,
and that is
PðA and BÞ¼ PðAÞ PðB j AÞ:

The reason is that when the events are independent PðBjAÞ¼ PðBÞ since
the occurrence of the first event A has no effect on the occurrence of the
second event B.