If p(a)=0.50, p()=0.40, and p(aub)=0.15 a=0.55 b=0.65 c=0.90 d=0.75

P(A ∩ B) = 0.75 (option d)

Step-by-step 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

step-by-step explanation:

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