I have been given the following Question.

Given that P(A) = 0.4 and P(AorB) = 0.9 Find P(B) if A and B are independent.

I know That if the're independent

P(A&B) = P(A)P(B)

P(AorB) = P(A) + P(B) - P(A&B)

And as the're independent

P(A|B) = P(A)

and

P(A|B) = P(A&B)/P(B)

As P(A&B) = P(A) + P(B) - P(A&B)

I know P(A) = 0.4, P(A|B) = 0.4 P(AorB)= 0.9 and

P(AorB) <= P(A) + P(B)

0.9 <= 0.4 + P(B)

Which implies that P(B) <= 0.5

I'm Trying to find P(B) however I'm having a lot of difficulty finding P(A&B).

Could someone please point me in the right direction of finding P(A&B)?

Kindest regards

Brendan