One bag contains 4 white balls and 3 black balls and a secondbag contains 3 whit

Question

One bag contains 4 white balls and 3 black balls and a secondbag contains 3 white balls and 5 black balls. One ball is drawn andplaced unseen in the second bag. What is the probability that aball now drawn from the second bag is black? I came up with 5 out of 9 that a black ball will be drawnfrom the second bag...am i on the right track or completely off?Any help would be greatly appreciated. Thank You. One bag contains 4 white balls and 3 black balls and a secondbag contains 3 white balls and 5 black balls. One ball is drawn andplaced unseen in the second bag. What is the probability that aball now drawn from the second bag is black? I came up with 5 out of 9 that a black ball will be drawnfrom the second bag...am i on the right track or completely off?Any help would be greatly appreciated. Thank You.

Explanation / Answer

For the first ball, P(W) = 4/7 and P(B) = 3/7 If we have a White ball in first pick, then P(W in 2nd pickgiven W) = 4/9 and P(B in 2nd pick given W) = 5/9 If we have a Black ball in first pick, then P(W in 2nd pickgiven B) = 6/9 and P(B in 2nd pick given B) = 3/9 Thus, the desired prob is probability = P(W)P(B in 2nd pick given W) + P(B)P(B in 2ndpick given B)                 = (4/7)(5/9) + (3/7)(3/9)                 = 29/63

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