Directions Use the information given to answer the questions

Directions: Use the information given to answer the questions below.

Suppose: Pr(A^B) = 1/4 Pr(A^not B?) = 1/3 Pr(not A^B) = 1/4 What is Pr(not A)? Suppose: Pr(A^B) = 1/4 Pr(A^not B?) = 1/3 Pr(not A^B) = 1/4 What is Pr(B)? Suppose A and B independent. A and B are independent. Pr(A^B) = 1/4 Pr(A) = Pr(B) What is Pr(A|B)?

Solution

Pr(A^B) = 1/4

Pr(A^~B) = 1/3

Pr(A^B) +Pr(A^~B) = Pr(A) = 1/4 + 1/3 = 7/12

Pr(~A)= 1-7/12 = 5/12

Pr(~A^B) = 1/4

Pr(A^B) + Pr(~A^B) = Pr(B) = 1/4 + 1/4 = 1/2

Pr(~B) = 1-1/2 = 1/2

Pr(A^B) = 1/4

Since A and B are independent events so Pr(A^B) = Pr(A) Pr(B)

Pr(A) = Pr(B)

=> Pr(A)² = 1/4

=> Pr(A) = 1/2 = Pr(B)

Pr(A/B) = Pr(A^B)/Pr(B) = 1/4 / 1/2 = 1/2