Question

Given P(A)=31/100,P(B)=33/50, and P(A∪Bᶜ)=2/5. Find P(A∩Bᶜ). a) 0.27 b) 0.25 c) 0.28 d) 0.23 e) 0 f) None of the above.

Answer 1

To find P(A∩Bᶜ), we can use the formula: P(A∩Bᶜ) = P(A) - P(A∪B). We are given P(A)=31/100, P(B)=33/50, and P(A∪Bᶜ)=2/5. Plugging in these values, we can find P(A∩Bᶜ) = -26/100 = -0.26. However, probabilities cannot be negative, so the answer is none of the above (f).

Step-by-step explanation:

To find P(A∩BṈ), we can use the formula:

P(A∩BṈ) = P(A) - P(A∪B)

We are given that P(A) = 31/100 and P(A∪BṈ) = 2/5. To find P(A∪B), we can use the formula:

P(A∪B) = P(A) + P(B) - P(A∩B)

We are also given that P(B) = 33/50. By plugging in these values, we can find:

P(A∪B) = (31/100) + (33/50) - (2/5)

Simplifying the expression, we get P(A∪B) = 31/100 + 66/100 - 40/100 = 57/100.

Now, we can substitute the value of P(A∪B) into the formula for P(A∩BṈ) to find:

P(A∩BṈ) = (31/100) - (57/100)

Simplifying the expression, we get P(A∩BṈ) = -26/100 = -0.26.

However, probabilities cannot be negative, so the answer is none of the above (f).