10.3 Define and Use Probability

VOCABULARY

Probability

A number from 0 to 1 that indicates the likelihood an event will occur

Theoretical probability

When all outcomes are equally likely, the number of outcomes in event A divided by the total number of outcomes

Odds

Used to measure the chances in favor of an event occurring or the chances against an event occurring

Experimental probability

A calculation of the probability of an event based on performing an experiment

Geometric probability

Probability found by calculating a ratio of two lengths, areas, or volumes

THEORETICAL PROBABILITY OF AN EVENT

When all outcomes are equally likely, the theoretical probability that an event A will occur is:

	Number of outcomes in event A
P(A)=	Total number of outcomes

The theoretical probability of an event is often simply called the probability of the event.

Complete the following exercises.

1. Using a standard deck of 52 playing cards, find the probability of drawing a red queen.

2. In Example 2, find the probability that 4 of the 7 male players on the baseball team bat first, in any order.

0.0707

ODDS IN FAVOR OF OR ODDS AGAINST AN EVENT

When all outcomes are equally likely, the odds in favor of an event A and the odds against an event A are:

		Number of outcomes in A
Odds in favor of event A	=	Number of outcomes not in A

Number of outcomes not in A

Odds against event A	=
		Number of outcomes in A

You can write the odds in favor of or against an event in

the form or in the form a:b

Example 3

Find odds

Marbles A marble is drawn from a bag containing 6 red, 12 yellow, and 9 black marbles. Find (a) the odds in favor of drawing a red marble and (b) the odds against drawing a black marble.

Solution

a. Odds in favor of drawing red 21

₌Number of red _{=_______=______,or__2__:__7__}

Number of non-red

2. Odds against drawing black

₌ Number of non-black_{=______= _____ or__2__:__7__}

^{Number of black}

EXPERIMENTAL PROBABILITY OF AN EVENT

When an experiment is performed that consists of a certain number of trials, the experimental probability of an event A is given by:

_{Number of trials where A occurs}

P(A) =

Total number of trials

Example 4

Find an experimental probability

Exam Grades Exam grades of students in a history class are shown in the bar graph. Find the probability that a randomly chosen student in this history class received a C or better.

Solution

The total number of students who took the test is:__ 3+1+8+12+7_= __31__

Of those surveyed, a C. __8+12+7__ = ____27__ received at least C

P(at least a C) =______»_0.871_

Complete the following exercises.

1. A marble is drawn from a bag containing 6 blue, 6 yellow, 9 white, and 11 green marbles. Find the odds in favor of drawing a yellow marble.

or 3:13