getting an outcome after x number of tries

ssmmss

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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.
 
(A) is correct.
(B) it is expectation. By definition E(X)=∑_i xi*pi
for your case xi=i, i=1,2,..10 (why 10?). pi is the probability that i-th time get red ball.
use method in (A) find pi.
 
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