Chapter 4, Problem 2LC

a

To determine

.

Check whether A and B cannot be independent if A and B are mutually exclusive.

Explain the answer and give an example.

b

To determine

Identify the condition under which $P\left(A\text{ and }B\right)=P\left(A\right)\times P\left(B\right)$ is true.

Identify the condition under which $P\left(A\text{ and }B\right)=P\left(A\right)\times P\left(B\right)$ is not true.

c

To determine

Check the condition under which $P\left(A\text{ or }B\right)=P\left(A\right)+P\left(B\right)$ is true.

Check the condition under which $P\left(A\text{ or }B\right)=P\left(A\right)+P\left(B\right)$ is not true.