Algebra 1 Common Core Student Edition, Grade 8-9

Does a "favorable
outcom e" always
mean that something
good happens?
No. For example, if you
are determining the
probability of losing a
game, the "favorable"
outcomes are the
outcomes where you
lose.

Astronomy Our solar system's 8 planets, in order o f least to greatest distance from

the sun, are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. You

will randomly draw on e of the nam es o f the planets and write a report on that planet.

What is the theoretical probability that you will select a planet w h ose distance from

the sun is less than Earth’s?

Fi n d i n g Th eo r et i cal Pr o b a b i l i t y

n _ number of favorable outcomes

■e v e n ) number of possible outcomes

Two planets o ut of 8 are nearer to the sun

than Earth: Mercury and Venus.

Simplify.

The probability of selecting a p lan et w hose distance from th e su n is less th a n

Earth’s is^4.

^ Got It? 1. In Problem 1, w h at is th e theoretical probability th at you will select a p lan et

w hose distance from th e su n is greater th a n Earth's?

The complement of an event consists of all outcom es in th e sam ple space th a t are not

in th e event. The possible outcom es for rolling a n u m b e r cube are 1, 2 ,3 ,4 , 5, a n d 6. The

outcom es for rolling an even n u m b e r are 2,4, a n d 6. T h e o u t c o m e s f o r t h e c o m p l e m e n t

of rolling an even n u m b e r are 1, 3, an d 5.

The sum of th e probabilities of a n event a n d its co m p lem en t is 1.

P(event) + P(not event) = 1 or P(not event) = 1 - P(event)

...................

How else can you

find P(not D rink A)?

You can divide the

number of other drink

samples by the total

number of samples.

P(not Drink A)

10 + 10 + 10

50

_ 30 _ 3

50 5

Pro b lem 2 Fi n d i n g t h e P r o b a b i l i t y o f t h e Co m p l e m e n t o f a n Ev e n t

Consumer Research In a taste test, 50 participants are randomly given a beverage

to sample. There are 20 sam ples of Drink A, 10 sam ples o f Drink B, 10 sam ples of

Drink C, and 10 sam ples of Drink D. What is the probability o f a participant not

getting Drink A?

P (Drink A) =

number of samples of Drink A

total number of samples

P (not Drink A) = 1 - P (Drink A)

20

50

= 1

Find P (D rinkA ).

Use the com plem ent form ula.

Substitute and simplify.

The probability of not getting Drink A is g.

sj) Got It? 2. Reasoning Suppose a taste test is re p eated w ith th e sam e n u m b e r of

sam ples of D rink A, b u t m ore sam ples of o th er drinks. W hat h ap p e n s to

P (n o t D rink A)?

770 Ch ap t er 12 Dat a An al ysi s an d Pr o b ab i l i t y