contestada

Urn A contains 8 yellow balls and 6 red balls. Urn B contains 3 yellow balls and 9 red balls. Urn C contains 4 yellow balls and 11 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) 0.2451 b) 0.0725 c) 0.2298 d) 0.0544 e) 0.5252 f) None of the above.

Respuesta :

nobillionaireNobley
Given that Urn A contains 8 yellow balls and 6 red balls. Urn B contains 3 yellow balls and 9 red balls. Urn C contains 4 yellow balls and 11 red balls.

The probability that a chosen ball came from urn B, given that it was a yellow ball is given by:

[tex]P(yellow|B)= \frac{P(B\, and\, yellow)}{P(B)} \\ \\ = \frac{\frac{1}{3}\times\frac{3}{12}}{\frac{1}{3}\times\frac{8}{14}+\frac{1}{3}\times\frac{3}{12}+\frac{1}{3}\times\frac{3}{15}} = \frac{\frac{1}{12}}{\frac{4}{21}+\frac{1}{12}+\frac{1}{15}} \\ \\ = \frac{\frac{1}{12}}{\frac{143}{420}} =\frac{35}{143}=0.2448[/tex]