Chapter 13, Problem 13CT

A cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

What is the probability that a bottle chosen at random is Coke?

What is the probability that a bottle chosen at random is either Pepsi or IBC?

To determine

To calculate: The probability that a bottle chosen at random is Coke, if a cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

Answer to Problem 13CT

Solution:

The probability that a bottle chosen at random is Cokeis $0.25$.

Explanation of Solution

Given information:

A cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

Formula used:

The formula to find probability for any event $E$ is;

$P\left(E\right)=\frac{\text{Number}\text{of}\text{ways}\text{that}\text{E}\text{can}\text{occur}}{\text{Number}\text{of}\text{possible}\text{outcomes}}$.

Calculation:

To calculate the probability that a bottle chosen at random is Coke, first calculate total number of bottles in a cooler.

A cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

Thus, the cooler contains total $8+5+4+3=20$ bottles.

Out of those 20 bottles, $5$ bottles are for Coke.

Thus, $P\left(\text{select}\text{cock}\text{bottle}\right)=\frac{\text{Number}\text{of}\text{Cock}\text{bottles}\text{in}\text{cooler}}{\text{Total}\text{number}\text{of}\text{bottles}\text{in}\text{cooler}}=\frac{5}{20}=0.25$

Therefore, the probability that a bottle chosen at random is Coke is $0.25$.

To determine

To calculate: The probability that a bottle chosen at random is either Pepsi or IBC. if a cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

Answer to Problem 13CT

Solution:

The probability that a bottle chosen at random is either Pepsi or IBC is $0.55$.

Explanation of Solution

Given information:

A cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

Formula used:

The formula to find probability for any event $E$ is;

$P\left(E\right)=\frac{\text{Number}\text{of}\text{ways}\text{that}\text{E}\text{can}\text{occur}}{\text{Number}\text{of}\text{possible}\text{outcomes}}$.

Calculation:

To calculate the probability that a bottle chosen at random is either Pepsi or IBC, first calculate total number of bottles in a cooler.

A cooler contains $8$ bottles of Pepsi, $5$ bottles of Coke, $4$ bottles of Mountain Dew, and $3$ bottles of IBC.

Thus, the cooler contains total $8+5+4+3=20$ bottles.

Out of those 20 bottles, $8$ bottles are for Pepsi and $3$ bottles are for IBC.

Thus, the number of bottles contains either Pepsi or IBC is $8+3=11$

Thus, $P\left(\text{either Pepsi or IBC}\right)=\frac{\text{Number of bottles contains either Pepsi or IBC}}{\text{Total}\text{number}\text{of}\text{bottles}\text{in}\text{cooler}}=\frac{11}{20}=0.55$.

Therefore, the probability that a bottle chosen at random is either Pepsi or IBCis $0.55$.