Chapter 0, Problem 22PR

To determine

Whether the events are independent or dependent and the probability for someone ordered item #345A also ordered item #345B.

Answer to Problem 22PR

Events are dependent.

The probability for someone ordered both the items is approx. 0.28.

Explanation of Solution

Given information:

18% of INET Clothing customers purchased item #345A.

5% of the customers order item #345A and item #345B.

Conditional Probability definition:

  $P\left(\text{B}|\text{A}\right)=\frac{P\left(\text{B}\text{and}\text{A}\right)}{P\left(\text{A}\right)}$

Since there are some customers ordered both the items, the events are dependent.

Now,

Probability for the customer purchased item #345A,

  $P\left(\text{\#345A}\right)=18\%=0.18$

Probability for the customer ordered item #345A and item #345B,

  $P\left(\text{\#345A}\text{and}\text{\#345B}\right)=5\%=0.05$

Then

Apply the conditional probability:

  $\begin{array}{l}P\left(\text{\#345B}|\text{\#345A}\right)=\frac{P\left(\text{\#345B}\text{and}\#345\text{A}\right)}{P\left(\text{\#345A}\right)}\\ =\frac{0.05}{0.18}\\ =\frac{5}{18}\\ \approx 0.28\\ =28\%\end{array}$

Thus,

Around 28% of the customers ordered item #345A and item #345B and the probability is approx. 0.28.