Question

Two events A and B are independent with Upper P left-parenthesis Upper A right-parenthesis equals Upper P left-parenthesis Upper B right-parenthesis equals 0.5. Then Upper P left-parenthesis Upper A intersection Upper B right-parenthesis is____________.

Answer 1

The value of P (A ∩ B) is 0.25.

Explanation:

Independent events are those events that do not effect the occurrence of each other, i.e. if event X and Y are independent then the occurrence of X and Y are not influenced by each other.

For independent events X and Y the joint probability of X and Y is:

`P (X\cap Y)=P(X)* P(Y)`

It is provided that events A and B are independent of each other.

And P (A) = P (B) = 0.50.

Compute the value of P (A ∩ B) as follows:

`P (A\cap B)=P(A)* P(B) \\= 0.50*0.50\\=0.25`

Thus, the value of P (A ∩ B) is 0.25.