Question

Checking independence Suppose C and D are two events such that

$P\left(C\right)=0.6,P\left(D\right)=0.45,$and $P(C\cap D)=0.3$Are events C and D independent? Justify your answer.

Short answer

The required answer is No

Step-by-step solution

Given information

Given,

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

Calculation

If the following condition is met, two events are said to be independent.

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

The above-mentioned condition can be checked as follows:

$$\begin{gathered} P(C\cap D)=P\left(C\right)\times P\left(D\right) \\ 0.3=0.45\times 0.6 \\ 0.3notequalto0.27 \end{gathered}$$

Hence, the above-mentioned condition is not satisfied.

Therefore, the two events $C$and $D$are not independent events.