Question

Suppose that a person selects a ball by rst picking one of two boxes at random and then selecting a ball from this box: The rst box contains three orange balls and four black balls. The second box contains ve orange balls and six black balls. What is the probability that the person picked from the second box given that they randomly picked an orange ball?

Answer 1

Explanation:

Given that A1 - picking from I box of 3 orange and 4 black balls and

A2 - picking from II box with 5 orange and 6 black balls

B - the randomly picked ball is orange

Required probability

`= P(A2/B)\\=(P(A2B))/(P(A1B)+P(A2B))` (Bayes theorem on conditional probability)

=
`((1)/(2)*(5)/(11)  )/((1)/(2)*(3)/(7) +(1)/(2)*(5)/(11) ) \\=(35)/(68)`