A bag contains n blue and m red marbles. You randomly pick a marble from the...

A bag contains n blue and m red marbles. You randomly pick a marble from the bag, write down its color, and then put the marble back in the bag. This process is repeated until you pick either two consecutive blue or two consecutive red marbles. Given that the process stopped because you picked two consecutive blue marbles, what is the probability that the first marble you picked was blue?

Please note that the question asks you to derive the probability of the overall first marble being blue. For example, you may draw 1000 marbles until you get two consecutive blue marbles. You need to derive the probability of the very first of these marbles being blue given that the last two marbles are blue.

Expert Solution

Theory of combination is below.

orchestra answered 2 years ago

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