Algebra 1 Common Core Student Edition, Grade 8-9

H o w is P (d rag o n a f t e r
dotted) different
from Pfdragon)?
After selecting the first
tile w ithout replacement,
there is one less tile
to choose from for the
second choice.

Key Concept Probability of Two Dependent Events

If A a n d B are d e p e n d e n t events, P{A then B) = P(A) • P(B after 21).

Selecting W ithout Replacem ent GRI D& ED RESPON SE

Games Suppose you ch oose a tile at random from the tiles shown in Problem 3.

Without replacing the first tile, you select a second tile. What is the probability that

you ch oose a dotted tile and then a dragon tile?

Because you do n o t replace th e first tile, th e events are d ep en d en t.

P(dotted) = 4 of the 15 tiles are dotted.

P (d ra g o n after dotted) = y j 3 of the 14 rem aining tiles are dragons.

P (d o tte d th e n dragon) = P (d o tte d ) • P (d ra g o n after dotted)

4 3 2

= 15 * 14 = 35 Substitute and then simplify.

The probability th a t you will choose a d o tted tile an d th e n a dragon tile is 35.

<§ Got If? 4. In Problem 4, w h at is th e probability th a t you will random ly choose a flower

an d then, w ithout replacing th e first tile, a bird?

2 /35

(/) (!)

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Finding the P robability of a Com pound Event

Essay C o ntest One freshman, 2 sophom ores, 4 juniors, and 5 seniors receive top

scores in a sch ool essay contest. To ch oose w hich 2 students will read their essays at

the town fair, 2 n am es are ch osen at random from a hat. What is the probability that

a junior and then a senior are chosen?

Grade levels of the

12 students

...Ne e d ........

P (junior then senior) Determine whether the events are dependent or

independent and use the formula that applies.

The first outcom e affects th e probability of th e second. So th e events are dep en d en t.

P(junior) = ^ | 4 o f the 12 students are juniors.

P(senior after junior) = — 5 of the 11 remaining students are seniors.

P (ju n io r th e n senior) -P(junior) • P (se n io r after junior)

= | • -jj = Substitute and then simplify.

The probability th a t a ju n io r a n d th e n a senior are ch o sen is33-

c

PowerAlgebra.com [ Lesson 12-8 Probability of Compound Events^779