Question

If P(A or B)= 0.9, P(A)=0.4, and P(B)=0.7, determine P(A and B) P(A and B)=

Answer 1

We are given the following information

P(A or B) = 0.9

P(A) = 0.4

P(B) = 0.7

We asked to find P(A and B)

Recall the formula

`P(A\cap B)=P(A)+P(B)-P(A\cup B)`

"and" means Intersection

"or" means Union

Let us substitute the given probabilities into the above formula

`P(A\cap B)=0.4+0.7-0.9=0.2`

Therefore, the probability P(A and B) is 0.2