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
[tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]"and" means Intersection
"or" means Union
Let us substitute the given probabilities into the above formula
[tex]P(A\cap B)=0.4+0.7-0.9=0.2[/tex]Therefore, the probability P(A and B) is 0.2
