Answer:
P(A ∩ B) = 0.75 (option d)
Explanation:
P(A)=0.50
P(B)=0.40
P(A U B)=0.15
P(A ∩ B)=?
P(A U B)=P(A)+P(B)-P(A ∩ B)
Replacing the given values:
0.15=0.50+0.40-P(A ∩ B)
Adding like terms:
0.15=0.90-P(A ∩ B)
Solving for P(A ∩ B):
Subtracting 0.90 both sides of the equation:
0.15-0.90=0.90-P(A ∩ B)-0.90
Subtracting:
-0.75 = -P(A ∩ B)
Multiplying both sides of the equation by -1:
(-1)(-0.75) = (-1) ( -P(A ∩ B) )
0.75 = P(A ∩ B)
P(A ∩ B) = 0.75