Question

Suppose Q and R are independent events. Find P (Q and R) if P(Q) = 4/7
and P(R) = 1/2

Answer 1

2/7

Explanation:

If two events A and B are independent, then P(A and B)=P(A)P(B).

So since Q and R are independent, then P(Q and R)=P(Q)P(R).

Let's substitute and evaluate:

`P(Q\text{ and }R)=P(Q)\cdot P(R)=(4)/(7) \cdot (1)/(2)=(4)/(14)`.

Both 2 and 14 are divisible by 2, so to reduce 4/14 we could divide top and bottom by 2:

4/14=(4/2)/(14/2)=2/7