Question

A box has 4 blue and 7 green jelly beans. A bag has 2 blue and 7 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

Baye's Theorem: P(A | B) = P(A & B)/P(B)

P(transferred jelly bean was green | green jelly bean is selected from bag) = P(transferred jelly bean was green and green jelly bean is selected from bag) / P(green jelly bean is selected from bag)

= P(transferred jelly bean was green and green jelly bean is selected from bag) / [P(transferred jelly bean was green and green jelly bean is selected from bag) + P(transferred jelly bean was blue and green jelly bean is selected from bag) ]

= (7/11 x 8/10)/[(7/11 x 8/10) + (4/11 x 7/10)]

= 0.667