Chapter 5.3, Problem 100E

To determine

To check: Whether the events C and D are independent or not.

Answer to Problem 100E

No.

Explanation of Solution

Given:

  $\begin{array}{l}P\left(C\right)=0.6\\ P\left(D\right)=0.45\\ P\left(C\cap D\right)=0.3\end{array}$

Concept used:

Two events are said to be independent, if following condition is satisfied

  $P\left(C\cap D\right)=P\left(C\right)\times P\left(D\right)$

Calculation:

Here, above mentioned condition could be checked as:

  $\begin{array}{c}P\left(C\cap D\right)=P\left(C\right)\times P\left(D\right)\\ 0.3=0.45\times 0.6\\ 0.3\ne 0.27\end{array}$

Since, above mentioned condition is not satisfied. Thus, the two events C and D are not independent events.