Question

A box has 2 blue and 9 green jelly beans. A bag has 9 blue and 2 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

We want, P(Transferred Jelly is green|Green jelly is selected from the bag)

Using Bayes theorem this is:

P(Transferred Jelly is green and Green jelly is selected from the bag)/P(Green jelly is selected from the bag)

Now, P(Green jelly is selected from the bag) = P(Transferred Jelly is green and green jelly is selected) + P(Transferred Jelly is blue and green jelly is selected)

Now, P(Transferred Jelly is green and green jelly is selected) = P(Transferred Jelly is green)*P(Green jelly is then selected) = 9/11*3/12= 0.20455 (Since after transferring 1 of the 9 green jellies from the box there are now 3 green jellies in the bag and any of it can be selected out of the total 12)

Similarly, P(Transferred Jelly is blue and Green jelly is selected from bag)= 2/11*2/12 = 0.03030

So Required Probability is: 0.20455/(0.20455+0.03030) = 0.8710

So the required probability is 0.8710