Chapter 10.2, Problem 16E

To determine

To explain:

The error of the given calculation of the probability and give the correct value

Answer to Problem 16E

The error of the given calculation is wrong value of the probability for the selection of heath magazine due to which the resulted value of the probability for both events is also wrong.

Thus the correct probability value for both events is $0.2857$ .

Explanation of Solution

Given information:

Event $A$ : Selection of first magazine of the fashion

Event $B$ : Selection of second magazine of health

  

In this question, the probability values of two independent events are given and then joint occurrence at the same time in the given figure of the calculation.

Here, given as: Two independent events are $A$ and $B$ . The error of the given calculation is wrong value of the probability for the selection of heath magazine due to which the resulted value of the probability for both events is also wrong.

Now the correct values probability for individual event:

  $\begin{array}{l}P\left(A\right)=\frac{3}{7}\\ P\left(B\right)=\frac{4}{6}\end{array}$

So, the correct method to calculate probability values of both events:

  $\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)\\ P\left(A\cap B\right)=\frac{3}{7}\times \frac{4}{6}\\ P\left(A\cap B\right)=0.2857\end{array}$