Question

Two computers A and B are to be marketed. A sales man who is assigned the job of finding customer for them as 60% and 40% chances respectively of succeeding for computer A and B. The two computers can be sold independently. Given that he was able to sell at least one computer.
1.what is the probability that computer A has been sold?.
2.what is the probability that computer B has been sold?.

Answer 1

1)P(A∪B)=P(A)+P(B)−P(A∩B)=0.6+0.4−0.24=0.76

$P(A | A\cup B) = \frac {P(A \cap(A\cup B))}{P(A\cup B)} = \frac{P(A)}{P(A\cup B)} = \frac{0.6}{0.76} = 0.789$

2)$P(B | A\cup B) = \frac {P(B \cap(A\cup B))}{P(A\cup B)} = \frac{P(B)}{P(A\cup B)} = \frac{0.4}{0.76} = 0.526$