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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鈥�R)

=P(Redbead|tossingaHeadonthecoin)P(tossingaHeadonthecoin)

=P(R|H)脳P(H)

=312脳23

=636

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