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CAF123
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Homework Statement
An urn contains 3 red and 7 black balls. A and B withdraw balls consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball.)
The Attempt at a Solution
A selects first => he will win with prob 3/10
B selects second => prob that he gets red is conditional on what colour A took.
P(B got red) = P(B got red| A got red)P(A got red) + P(B got red| A not got red)P(A not red) = (2/9)(3/10) + (3/9)(7/10) = 3/10. This seems nonintuitive - it seems the prob of B getting red is independent of what A took. Can someone explain this?
Where to go from here?