Chapter 10.1, Problem 33E

Solution

To calculate: The probability that both are big bombs if two cars are selected at random.

The probability that both are big bombs is $\frac{19}{30}$ .

Given information:

Floppy Jalopy Rent-a-Car has $25$ cars available for rental- $20$ big bombs and $5$ midsize cars.

Calculation:

The formula used to calculate the probability of an event occurring is:

  $P=\frac{N(\text{possible outcomes})}{N(\text{desirable outcomes})}\text{}$

As there are  $9$  papers, it concludes that:

  $\begin{array}{l}P(\text{first big bomb})=\frac{20}{25}\text{}\\ =\frac{4}{5}\text{}\end{array}$

If a big bomb is picked out, there will be  $24$  remaining cars and  $19$  big bombs, so:

  $P(\text{second big bomb})=\frac{19}{24}$

The probability of two events happening simultaneously is calculated by multiplying the probability of each event occurring.

We use this to calculate the probability of choosing two big bombs:

  $\begin{array}{l}P(\text{two big bombs})=\frac{4}{5}\times \text{}\frac{19}{24}\\ =\frac{19}{30}\text{}\text{}\end{array}$

Hence, probability that both are big bombs if two cars are selected at random is $\frac{19}{30}$ .