Probability And Statistics Worksheets Page 13
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429-3
Compound
Events
■
Goals
Find probabilities of compound events.
Applications
Sports, Games, Business
Play this game with a partner. Use a pair of 6-sided dice.
1. Player A rolls first. If Player A rolls a 7, Player B wins
the game. If not, Player B rolls.
2. If Player B rolls a 7 or an 11, Player A wins. If not, it is
Player A’s turn. Continue taking turns until there is a winner.
3. Play the game several times. Do you think one player
has a better chance of winning?
B
U
UILD
NDERSTANDING
A compound event consists of two or more simple events. Compound events may
involve finding the probability of one event and another event occurring. Or, the
probability of one event or another event occurring. For example, when rolling a
die, rolling a number that is even (event A) and greater than 2 (event B) is written
P(A and B). Rolling a number that is even or greater than 2 is written P(A or B).
If two events cannot occur at the same time, they are called mutually exclusive
events. For example, it is impossible to draw from a standard deck of playing
cards a card that is both a heart and a club.
When two events A and B are mutually exclusive, the probability of the
compound event A or B can be found using the formula P(A or B)
P(A)
P(B).
E x a m p l e 1
SPORTS
A standard deck of playing cards is used to simulate a baseball game.
During the game, players draw a card at random. Spade number cards greater
than 4 represent doubles. Home runs are represented by either a 3 or a queen.
a. Find P(spade and a number card greater than 4).
b. Find P(3 or queen).
Solution
There are 52 possible outcomes.
a. There are 6 outcomes in which spades are greater than 4: 5, 6, 7, 8, 9, and 10 of
spades.
6
3
So, P(spade and number greater than 4)
or
.
5
2
2
6
3
The probability that the card will be a spade and a number greater than 4 is
.
2
6
392
Chapter 9 Probability and Statistics
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