Algebra 1 Common Core Student Edition, Grade 8-9

@ Common Core State Standards

IlK / S-CP.B.7 Apply th e Addition Rule,

I l O D C I D I I I T y o r P(A or fi) = P(A) + P( B) - P(A and B) , and interpret

Compound Events

the answer in terms o f the model. Also S-CP.B.8

MP 1, MP 2, M P 3 , M P 4, M P 6

Object ives To find probabilities of m utually exclusive an d overlapping events

To find probabilities of in d e p e n d e n t an d d e p e n d e n t events

Artist Category Songs

Absolute Value Rock 10

Algebras Pop^12

Arithmetics Rock 6

FOILs Pop 5

Pascal's Triangle Country 12

Pi Rock^11

Start with a plan.

How many songs

are there?

MATHEMATICAL

PRACTICES

f Getting Ready!

The portable music player at t he right

is set t o choose a song at random f rom

the playlist. What is the probability

that the next song played is a rock

so n g b y an a r t i s t w h o se n am e b eg i n s

with the let t er A? How did you find

your answer?

Lesson

Vocabulary

compound event

mutually

exclusive events

overlapping

events

in d e p e n d e n t

events

dependent

events

In the Solve It, you found th e probability th at th e next song is b o th a rock song an d

also a song by an artist w hose n am e begins w ith the letter A. This is an exam ple of a

compound event, w hich consists of two or m ore events linked by th e w ord and or the

word or.

Esse n t i a l U n d e r st a n d i n g You can write th e probability of a co m p o u n d event as

an expression involving probabilities of sim pler events. This m ay m ake the co m p o u n d

probability easier to find.

W hen two events have no outcom es in com m on, th e events are mutually exclusive

events. If A and B are m utually exclusive events, th e n P{A and B) = 0. W hen events

have at least one outcome in common, they are overlapping events.

You n ee d to determ ine w h e th e r two events A and B are m utually exclusive before you

can find P (A or B).

Key Concept Probability of A or 6

Probability of M utually Exclusive Events

If A an d B are m utually exclusive events, P{A or B) P(A) + P(B).

Probability of Overlapping Events

If A and B are overlapping events, P[A or B) = P[A) + P(B) — P[A and B).

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