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:0.833Step-by-step 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.[tex]P(A_1) = \frac{2}{11} \\P(A_2) = \frac{9}{11}[/tex]Let B be the event that the jelly bean selected from the bag was green.[tex]P(B) = P(A1B)+P(A2B)\\= \frac{2}{11}\frac{9}{13}+ \frac{9}{11}\frac{10}{13}\\=\frac{108}{143}[/tex]Required probability = P(A2/B) =[tex]\frac{P(A2B)}{P(B)} \\=\frac{90/143}{108/143} \\= \frac{5}{6}[/tex]=0.833