Suppose Q and R are independent events, and P(Q) = 0.45, P(R) = 0.31. Find P(Q and R)?

Solution:

Given Q and R are independent events and P(Q) = 0.45, P(R) = 0.31

We know that if two events are independent to each other then the probability of intersection of them is equal to the product of their individual probability.

So, in P(Q and R) , ‘and’ denotes the intersection or common between the two events.

P(Q ∩ R) = P(Q) × P(R)

P(Q ∩ R) = (0.45) × (0.31)

P(Q ∩ R) = 0.14

P(Q and R) = 0.14

Suppose Q and R are independent events, and P(Q) = 0.45, P(R) = 0.31. Find P(Q and R)?

Summary:

If Q and R are independent events, and P(Q) = 0.45, P(R) = 0.31 then P(Q and R) = 0.14