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10 red marbles and 10 blue marbles are placed into a bag. All mixed up and randomly selecting one after the other with replacement, until a red marble is selected.

a) What is the probability that the first time that a red marble is pulled is on 6th try? My answer:

Probability of drawing a red marble on the 6th try is: (.5)^5 * (.5)^1 = 0.015625

b) On average, how many marbles will we have to pull in order to get a red marble? My answer: 1/p = 1/.5 = 2

If my answer to question (b) is correct, is this what we call math expectation.

Thanks.

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  • $\begingroup$ Yes, the answers are correct. And yes, if random variable $X$ is the number of trials until the first red, then the expectation $E(X)$ of $X$ is $2$. The term "average" is somewhat ambiguous, since there are several notions of average. But expectation is undoubtedly intended here. $\endgroup$ – André Nicolas Jun 12 '14 at 4:54

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