If a green jelly bean is selected from the bag, what is the probability that the transferred jelly bean was green?

Question

A box has 5 blue and 2 green jelly beans. A bag has 2 blue and 5 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?

Answer 1

You are looking for the P(Green transferred from box| Green chosen from bag)

Bayes: P(G t B| G c b) = P(G c )| G t B) P(G t B)/P(G c b) Where B is Box, b is bag and c and t mean chosen and transferred

P(G t B) = 2/7

If the G is transferred, the bag will have 2B and 6G and the probability of picking the G is 6/8 = 3/4

The numerator is now: 2/7*3/4 = 3/14

In order to find the denominator you need to add P(green|green transfer) + P(green|blue transfer)

We just did the first term as that is the numerator.

The second term will be P(blue trans)*P(G after blue trans) = 5/7*(5/8) = 25/56 (similar logic to above)

Prob = 3/14 / (3/14 + 25/56) = 12/(12+25)

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