A box has 8 blue and 5 green jelly beans. A bag has 6 blue and 8 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?

Question

A box has 8 blue and 5 green jelly beans. A bag has 6 blue and 8 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

To find the probability that the transferred jelly bean was green, given that a green jelly bean was selected from the bag, we can use conditional probability.

Conditional probability is the probability of an event (in this case, the transferred jelly bean being green) occurring given that another event (in this case, a green jelly bean being selected from the bag) has already occurred.

Let's break down the problem step by step to find the solution:

Step 1: Calculate the probability of selecting a green jelly bean from the bag.
The bag has a total of 6 blue and 8 green jelly beans, so the probability of selecting a green jelly bean from the bag is 8/(6+8) = 8/14 = 4/7.

Step 2: Calculate the probability of selecting a green jelly bean from the box and transferring it into the bag.
The box has a total of 8 blue and 5 green jelly beans, so the probability of selecting a green jelly bean from the box is 5/(8+5) = 5/13.

Step 3: Calculate the probability of both events occurring (i.e., a green jelly bean being selected from the bag and transferring a green jelly bean from the box to the bag).
The probability of both events occurring is the product of the individual probabilities: (4/7) * (5/13) = 20/91.

Step 4: Calculate the conditional probability that the transferred jelly bean was green, given that a green jelly bean was selected from the bag.
The conditional probability is given by the formula: P(A|B) = P(A and B) / P(B), where A is the event of selecting a green jelly bean from the box and transferring it to the bag, and B is the event of selecting a green jelly bean from the bag.

Plugging in the values, we have: P(A|B) = (20/91) / (4/7) = (20/91) * (7/4) = 140/364 ≈ 0.385.

Therefore, the probability that the transferred jelly bean was green, given that a green jelly bean was selected from the bag, is approximately 0.385, or 38.5%.

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To find the probability that the transferred jelly bean was green, given that a green jelly bean was selected from the bag, we can use conditional probability.