Question

Past attendance records show that the probability that the chairman of the board attends a meeting is 0.65, that the president of the company attends a meeting is 0.9, and that they both attend a meeting is 0.6. Would you say that the chairman and the president act independently
regarding their attendance at the meetings of the board of directors? Why?

Answer 1

The events A and B are independent if and only if (iff)

$$P(A\cap B)=P(A)\cdot P(B)$$

Let $A$ be the event, that the chairman of the board attends a meeting, $B$ be the event, that the president of the company attends a meeting.

Given that $P(A)=0.65, P(B)=0.9, P(A\cap B)=0.6$

Check the independence

$$P(A)\cdot P(B)=0.65\cdot0.9=0.585\not=0.6=P(A\cap B)$$

Therefore, the chairman and the president don't act independently regarding their attendance at the meetings of the board of directors.