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Chapter 3: Q. 114 (page 230)

Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red(R),four yellow(Y)and five blue(B)beads. For the coin, localid="1649537434462" P(H)=23andlocalid="1649537225213" P(T)=13wherelocalid="1649537596463" His heads andlocalid="1649537603746" Tis tails .

Find localid="1649537612097" P( tossing a Head on the coin AND a Red bead )

a. 23

b.515

c. 636

d. 536

Short Answer

Expert verified

P(tossingaHeadonthecoinANDaredbead)is636,So answer c is correct.

Step by step solution

01

Given data

From tree diagram,

Probability of tossing head on the coin P(H)=13.

Probability of tossing head on the coin with red beadP(R|H)=312.

Probability of tossing tail on the coinP(T)=13.

02

Calculation of P(tossing a Head on the coin AND a red bean)

Probability is,

P(tossingaHeadonthecoinANDaredbean)=>P(HAND R)

=P(Redbead|tossingaHeadonthecoin)P(tossingaHeadonthecoin)

=P(R|H)×P(H)

=312×23

=636

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Most popular questions from this chapter

A jar of 150 jelly beans contains 22 red jelly beans, 38

yellow, 20 green, 28 purple, 26 blue, and the rest are orange.

Let B = the event of getting a blue jelly bean

Let G = the event of getting a green jelly bean.

Let O = the event of getting an orange jelly bean.

Let P = the event of getting a purple jelly bean.

Let R = the event of getting a red jelly bean.

Let Y = the event of getting a yellow jelly bean.

Find P(P).

A box is filled with several party favors. It contains 12

hats, 15 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(F).

The following table of data obtained from www.baseball-almanac.com shows hit information for four players. Suppose that one hit from the table is randomly selected.

Are "the hit being made by Hank Aaron" and "the hit being a double" independent events?

a. Yes, because P(hit by Hank Aaron | hit is a double) =P(hit by Hank Aaron)

b. No, because P(hit by Hank Aaron | hit is a double) ≠P(hit is a double)

c. No, because P(hit is by Hank Aaron | hit is a double) ≠P(hit by Hank Aaron)

d. Yes, because P(hit is by Hank Aaron | hit is a double) =P(hit is a double)

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E OR M) mean in words?

Write the symbols for the probability that of all the outfielders, a player is not a great hitter.
See all solutions

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