urn a contains 6 yellow balls and 11 red balls. urn b contains 9 yellow balls and 10 red balls. urn c contains 11 yellow balls and 3 red balls. an urn is picked randomly (assume that each urn is equally likely to be chosen), and then a ball is picked from the selected urn. what is the probability that the chosen ball came from urn b, given that it was a yellow ball? a) 0.2938 b) 0.0645 c) 0.2189 d) 0.4873 e) 0.0620 f) none of the above.

Question

contestada

Respuesta :

ayune ayune · Answer 1 · 2022-11-26T12:43:41+01:00

There are three urns, A, B, and C. The probability that the chosen ball came from urn B, given that it was yellow is 0.3036

The formula for the conditional probability is:

P(A|B) = [P(B |A) P(A)] / P(B)

Where:

P(A |B) is read as probability of A given B occurs.

In the given problem:

Urn A contains 6 yellow balls + 11 red balls

Urn B contains 9 yellow balls + 10 red balls

Urn C contains 11 yellow balls + 3 red balls

Total balls = 50

total yellow balls = 26

Applying the conditional probability, the probability that the chosen ball came from urn B, given that it was yellow is P(B | yellow)

P(B | yellow) = [ P(yellow | B) P(B)] / P(yellow)

P(B) = 1/3

P(yellow | B) = 9/19

P (yellow) = 26/50

Hence,

P(B | yellow) = [9/19 x 1/3] / (26/50)

= 0.3036

Therefore, the probability that the chosen ball came from urn B, given that it was yellow is 0.3036

Learn more about probability here:

https://brainly.com/question/24299308

#SPJ4