Question

Let P(A)=0.65, P(B)=0.30, and P(AIB)=0.45

a. calculate P(AnB).
b. calculate P(AUB).
c. calculate P(BA)>

Answer 1

a. P(A AND B) = 0.135, b. P(A OR B) = 0.815, c. P(B|A) ≈ 0.208

Step-by-step explanation:

a. To find P(A AND B), we can use the formula P(A AND B) = P(A|B) * P(B).

Since we are given P(A|B) = 0.45 and P(B) = 0.30, we can substitute these values into the formula to get P(A AND B) = 0.45 * 0.30 = 0.135.

b. To find P(A OR B), we can use the formula P(A OR B) = P(A) + P(B) - P(A AND B).

Since we are given P(A) = 0.65, P(B) = 0.30, and P(A AND B) = 0.135, we can substitute these values into the formula to get P(A OR B) = 0.65 + 0.30 - 0.135 = 0.815.

c. To find P(B|A), we can use the formula P(B|A) = P(A AND B) / P(A).

Since we are given P(A AND B) = 0.135 and P(A) = 0.65, we can substitute these values into the formula to get P(B|A) = 0.135 / 0.65 ≈ 0.208.