Chapter 13, Problem 13CT

a.

To determine

The probability that the bottle chosen at random is coke.

Answer to Problem 13CT

The probability that the bottle chosen at random is cokeis $\frac{1}{4}$ .

Explanation of Solution

Given:

A cooler contain 8 bottles od pepsi, 5 bottles of coke, 4 bottles of mountain dew, and 3 bottles of IBC

Calculation:

Let pepsi bottle be A

Let coke bottle be B

Let mountain dew bottle be C

Let IBC bottle be D

Number of favourable events = 20

Therefore,

The probability that the bottle chosen at random is coke is,

  $\begin{array}{l}\Rightarrow P(B)=\frac{5}{20}\\ \Rightarrow P(B)=\frac{1}{4}\end{array}$

Hence,the probability that the bottle chosen at random is coke is $\frac{1}{4}$ .

b.

To determine

The probability that the bottle chosen at random is Pepsi or IBC.

Answer to Problem 13CT

The probability that the bottle chosen at random is Pepsi or IBC is $\frac{11}{20}$ .

Explanation of Solution

Given:

A cooler contain 8 bottles odpepsi, 5 bottles of coke, 4 bottles of mountain dew, and 3 bottles of IBC

Calculation:

Let pepsi bottle be A

Let coke bottle be B

Let mountain dew bottle be C

Let IBC bottle be D

Number of favourable events = 20

Therefore,

The probability that the bottle chosen at random is Pepsi or IBC is,

  $\begin{array}{l}P(A\cup D)=P(A)+P(D)-P(A\cap D)\\ \Rightarrow P(A\cup D)=(\frac{8}{20})+(\frac{3}{20})-0\\ \Rightarrow P(A\cup D)=\frac{11}{20}\end{array}$

Hence,probability that the bottle chosen at random is Pepsi or IBC is $\frac{11}{20}$ .