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You select a marble without looking and then put it back. If you do this 42 times, what is the

best prediction possible for the number of times you will pick a marble that is not green?
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User Eric Mamet
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Assuming that the marbles are either green or not green and that the probability of picking a green marble is constant on every trial, we can use probability to make a prediction.

Let p be the probability of picking a non-green marble on one trial, then the probability of picking a green marble is 1 - p.

Since we pick marbles with replacement, each trial is independent of the others, and the probability of picking a non-green marble is the same for every trial.

The number of times we pick a non-green marble in 42 trials follows a binomial distribution with parameters n = 42 and p.

The expected value (or mean) of a binomial distribution is given by np, so in this case, the best prediction for the number of times we will pick a non-green marble is:

42 * p

We don't know the value of p, but if we assume that the probability of picking a non-green marble is 1/2 (i.e., the marbles are evenly split between green and non-green), then the best prediction for the number of times we will pick a non-green marble is:

42 * (1/2) = 21

Therefore, the best prediction possible for the number of times you will pick a marble that is not green is 21.

User Danny
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