Question

A box has 2 blue and 9 green jelly beans. A bag has 3 blue and 9 green jelly beans. A jelly bean is selected at random from the box and placed in the bag. Then a jelly bean is selected at random from the bag. If a green jelly bean is selected from the bag, what is the probability that the transferred jelly bean was green? (Round your answer to three decimal places.)

Answer 1

0.833

Explanation:

Given that a jelly bean is seclted at random from the box and placed in the bag. This one can be either blue or green.

A1 - If blue is selected and put in the bag, then bag would have 4 blue and 9 green now.

A2 -If green is selected and put in the bag, then bag would have 3 blue and 10 green now.

`P(A_1) = (2)/(11) \\P(A_2) = (9)/(11)`

Let B be the event that the jelly bean selected from the bag was green.

`P(B) = P(A1B)+P(A2B)\\= (2)/(11)(9)/(13)+ (9)/(11)(10)/(13)\\=(108)/(143)`

Required probability = P(A2/B) =
`(P(A2B))/(P(B)) \\=(90/143)/(108/143) \\= (5)/(6)`

=0.833