Algebra 1 Common Core Student Edition, Grade 8-9

How many multiples
are there?
There are 10 multiples of
2:2,4, 6, 8,10,12,14,
16,18, and 20. There are
4 multiples of 5: 5,10,
15, and 20. There are 2
multiples of 2 and 5:10
and 20.

Mutually Exclusive and Overlapping Events

Suppose you spin a spinner that has 20 equal-sized sections num bered from 1 to 20.

0 What is the probability that you spin a 2 or a 5?

B ecause the sp in n er ca n n o t lan d on b o th 2 a n d 5, th e events are m utually exclusive.

P{2 or 5) = P (2) + P (5)

~20 + 20 Substitute.

=h =h simp|ify-

The probability th at you spin a 2 or a 5 is

0 What is the probability that you spin a num ber that is a m ultiple o f 2 or 5?

Since a n u m b e r can be a m ultiple of 2 an d a m ultiple of 5, such as 10, th e events

are overlapping.

P (multiple of 2 or multiple of 5)

= /’(multiple of 2) + P(m ultiple of 5) — ^(m ultiple of 2 and 5)

= i + Substitute.

= | § = § Simplify.

o

The probability th a t you spin a n u m b e r th a t is a m ultiple of 2 or a m ultiple of 5 is =.

Got It? 1. Suppose you roll a s tan d ard n u m b e r cube.

a. W hat is the probability th a t you roll an even n u m b e r or a n u m b e r less

than 4?

b. W hat is th e probability th a t you roll a 2 or an odd n um ber?

A stan d ard set of checkers h as equal n u m b e rs of red a n d black

checkers. The diagram at the right shows th e possible outcom es

w h e n random ly choosing a checker, p utting it back, an d choosing

again. The probability of getting a red on eith er choice is The

first choice, or event, does n o t affect th e seco n d event. The events

are independent.

Two events are independent events if th e occurrence of one event does n o t affect the

probability of th e seco n d event.

................................... ..................... — — — _ _ _ _ _ s

Key Concept Probability of Two Independent Events

in d e p e n d e n t events, P{A and B) = P(A) • P{B).

J

If A and B arc

1st Choice

Red

Black

2nd Choice

Red

Black

PowerAlgebra.com Lesso n 12- 8 Pr o b ab i l i t y o f Co m p o u n d Even t s^777