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mathinator mathinator
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Posts: 60
Rep: 2 0
7 years ago
Urn A contains 6 white marbles and 4 red marbles. Urn B contains 3 red marble sand two white marbles. A marble is selected at random from urn A, and then placed in urn B. Finally, a table is selected at random from urn B. What is the probability that the marbles selected from urn A was red, given that the marble selected from urn B is red?
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Staff Member
7 years ago
Urn A                                      .                                  Urn B
                                                .
6/10    ------------------------>     W   --------------------------- 3/6 ------------------>w
                                                     --------------------------- 3/6 ------------------>R
                                               .
                                               .
4/10    ------------------------>     R  --------------------------- 2/6 ------------------>w
                                                    --------------------------- 4/6 ------------------>R

A } 6w, 4r
B } 2w, 3r

P (red from A/red from B)= P(red B/red A) P(red A)/ P(red B)
                                              = [(4/6) x (4/10)] / [(3/6) x (6/10) x (4/6) x (4/10)]
                                              = (4/15) / [(3/10) x (4/15)] = 0.4706
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