Question

A distribution that represents the number of cars X parked in a randomly selected residential driveway on any night is given by

Given that there is at least 1 car parked on a randomly selected residential driveway on a particular night, which of the following is closest to the probability that exactly $4$cars are parked on that driveway?

a. $0.10$

b. $0.15$

c. $0.17$

d.$0.75$

e.$0.90$

Short answer

The answer is option (c)$0.17.$

Step-by-step solution

Given information

The given data is

Explanation

Let $X$be the total number of parked autos. As a result, we may deduce that

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

Using the complement rule as a guide,

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

The conditional probability is now computed as follows:

$$\begin{gathered} =\frac{P(X=4\text{and}X\ge 1)}{P(X\ge 1)} \\ =\frac{0.15}{0.90} \\ =0.17 \end{gathered}$$

As a result, option is the proper choice (c).