Question

There are two urns. The first one has 15 red balls and 5 black balls. The second one contains 14 red balls and 6 black balls. We choose randomly one of the urns, each of them equally likely to be chosen, and then we pick three balls from that urn (without replacement). It turns out that we have 3 red balls. Given that, what is the probability that we picked them from the second urn? Possible Answers A 1/2 B 4/9 C (29 choose 3) / (40 choose 3) D 14/29 E 28/29

          There are two urns. The first one has 15 red balls and 5 black balls. The second one contains 14 red balls and 6 black balls. We choose randomly one of the urns, each of them equally likely to be chosen, and then we pick three balls from that urn (without replacement). It turns out that we have 3 red balls. Given that, what is the probability that we picked them from the second urn?

Possible Answers
A 1/2
B 4/9
C (29 choose 3) / (40 choose 3)
D 14/29
E 28/29

There are two urns. The first one has 15 red balls and 5 black balls. The second one contains 14 red balls and 6 black balls. We choose randomly one of the urns, each of them equally likely to be chosen, and then we pick three balls from that urn (without replacement). It turns out that we have 3 red balls. Given that, what is the probability that we picked them from the second urn?

Possible Answers
A 1/2
B 4/9
C (29 choose 3) / (40 choose 3)
D 14/29
E 28/29

Added by Christopher A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

02/23/2023

Step 1

- B: We choose the second urn. - C: We pick 3 red balls. We want to find the probability P(B|C), which is the probability that we picked the balls from the second urn given that we have 3 red balls. Using Bayes' theorem, we have: P(B|C) = P(C|B) * P(B) / Show more…

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There are two urns. The first one has 15 red balls and 5 black balls. The second one contains 14 red balls and 6 black balls. We choose randomly one of the urns, each of them equally likely to be chosen, and then we pick three balls from that urn (without replacement). It turns out that we have 3 red balls. Given that, what is the probability that we picked them from the second urn? Possible Answers A 1/2 B 4/9 C (29 choose 3) / (40 choose 3) D 14/29 E 28/29