Chapter 12, Problem AP4.22CPT

To determine

To find out which of the following is closest to the probability that exactly four cars are parked on that driveway.

Answer to Problem AP4.22CPT

Option (c) is the correct option.

Explanation of Solution

It is given that there is at least one car parked on a randomly selected residential driveway on a particular night. Also, it is given,

x	0	1	2	3	4
p	0.1	0.2	0.35	0.2	0.15

Let X represents the number of cars parked. Then, we know that

  $\begin{array}{l}P(X=0)=0.10\\ P(X=4)=0.15\end{array}$

By using the compliment rule,

  $\begin{array}{l}P(X\ge 1)=1-P(X=0)\\ =1-0.10\\ =0.90\end{array}$

Now, the conditional probability will be calculated as:

  $\begin{array}{l}P(X=4|X\ge 1)\\ =\frac{P(X=4\text{ and }X\ge 1)}{P(X\ge 1)}\\ =\frac{0.15}{0.90}\\ =\frac{15}{90}\\ =0.17\end{array}$

Thus, the correct option is option (c).