Cant Solve this can anyone help?

Question

you select a marble without looking and then put it back. if you do this 12 times, what is the best prediction possible for the number of times you will pick a blue marble.

Answer 1

In order to give the best mathematical answer, we need more information from the problem. If all of the marbles are blue, then you will pick a blue marble every single time. If there are two colors of marbles in the bag, and there are even amounts of each marble in the bag, then the probability of you picking a blue marble each time, 12 times, is (1/2)^12. In general, for the general case, we will let the probability of picking a blue marble out of the bag be equal to p. The probability of you picking a blue marble once is p, and then picking a blue marble any time after that is p^n, where n=number of times in a row you pick a marble. You can construct a probability tree, wherein you list every possible combination of marble draws for each successive turn, to get all of the cases and possibilities of picking blue marbles and when you will pick them. You can also construct an expected value for this to try to deduce what the average number of times you will pick a blue marble will be, and this expected value will rely on the specific probabilities of picking a blue marble as well as picking other marbles. Without much more context for the problem, however, there isn't much more for an answer that I can give. I do hope this helps however!