Chapter 10.2, Problem 15E

To determine

To explain:

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

Answer to Problem 15E

The error is the addition of the individual probability values. Thus the correct probability value for both events is $0.12$ .

Explanation of Solution

Given information:

  

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 $B$ .

In the given calculation, the resulted probability of both events $A$ and $B$ is calculated by taking addition of the probability value of individual is the error.

If there is need to calculate the probability of event $A$ and $B$ then need to take multiplication of both events’ probability values. So, the correct probability of both events $A$ and $B$ calculated as:

  $\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)\\ P\left(A\cap B\right)=0.6\times 0.2\\ P\left(A\cap B\right)=0.12\end{array}$