Let PA 048 PB A 035 and PB Ac 010 Use a probability tre

Let P(A) = 0.48, P(B | A) = 0.35, and P(B | A^c) = 0.10. Use a probability tree to calculate the following probabilities: (Round your answers to 3 decimal places.)

Solution

a)

P(Ac) = 1 - P(A) = 1 - 0.48 = 0.52 [answer]

b)

P(A n B) = P(B|A) P(A) = 0.35*0.48 = 0.168 [answer]

c)

P(Ac n B) = P(B|Ac) P(Ac) = 0.10(0.52) = 0.052 [answer]

d)

P(B) = P(A n B) + P(Ac n B) = 0.168 + 0.052 = 0.22 [answer]

e)

P(A|B) = P(A n B) / P(B) = 0.168/0.22 = 0.763636364 [answer]