An urn contains 9 balls, one marked WIN and the others marked LOSE. You and another...

An urn contains 9 balls, one marked WIN and the others marked LOSE. You and another player take turns selecting a ball at random from the urn, one at a time. The first person to select the WIN ball is the winner. If you draw first, find the probability that you will win if the sampling is done without replacement?

My answer 3/9 is apparently incorrect.

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Expert Solution

The answer is 5/9.I can win at the draw 1,3,5,7,9.If I win in the first draw it is 1/9 probability.If I win in the 3rd draw which means I am losing at the 1st draw,my opponent is losing the 2nd draw with corresponding probablities 8/9 and 7/8(since 8 balls are left out of which 7 are losing and 1 is winning) and henceforth the events being independent the probability of me winning is (8/9*7/8*1/8)=1/9 and so on.All the probabilties will be 1/9 in a similar fashion adding to 5/9 for 5 possible winning draws.

orchestra answered 1 year ago

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