Urn A contains 4 white balls and 6 black balls. Urn B contains 3 white balls and
ID: 3436815 • Letter: U
Question
Urn A contains 4 white balls and 6 black balls. Urn B contains 3 white balls and 5 black balls. A ball is drawn from urn A and then transferred to urn B. After that a ball is drawn from urn B. What is the probability the transferred ball was black given that the second ball drawn was white? (Round your answer to the nearest hundredth.)
I know the answer is 0.53, and I'm supposed to solve using tree diagrams. I just have no idea how this problem was solved. Step by step explanations would be helpful?! Thank you!
Explanation / Answer
The given data can be presented like this.
The first ball drawn from urn A can be black or white
P(B) = 6/10 and P(W) = 4/10
If Black ball is taken and transferred urn B contains 3 white and 6 black balls.
Hence P(Second ball White) = 3/9
Joint prob for I one black and second white = 18/90 = 1/5=0.2
--------------------------------
Similarly joint prob for 1 white from First and second white
= 4/10(4/9) = 8/45
Total prob = 1/5+8/45=17/.45
= 0.38
= 14/45
Urn A B Black 6 5 white 4 3Related Questions
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