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