Homework SourseLet PA 054 PB A 041 and PB Ac 017 Use a probability tre
Let P(A) = 0.54, P(B | A) = 0.41, and P(B | Ac) = 0.17. Use a probability tree to calculate the following probabilities: (Round your answers to 3 decimal places.)
| a. P(Ac) | |
| b. P(A B) | |
| P(Ac B) | |
| c. P(B) | |
| d. P(A | B) | |
Solution
P(Ac) = 1 - 0.54 = 0.46
P(A and B ) = P(B/A) * P(A) = 0.41 * 0.54 = 0.2214
P(Ac and B) = P(B/Ac) * P(Ac) = 0.17*0.46 = 0.0782
P(B and Ac) = P(B) - P(B and A )
P(B) = 0.2214 + 0.0782 = 0.2996
P(A/B) = P(A and B) / P(B) = 0.2214 / 0.2996 = 0.738985
