Question

You select a marble without looking and then put it back. If you do this 11 times, what is the best prediction possible for the number of times you will pick a purple marble?

there is 11 marbles in total and only 7 purple marbles

Answer 1

Explanation:

If there are 11 marbles in total and 7 of them are purple, then the probability of picking a purple marble on any given draw is 7/11. However, since we are drawing 11 times with replacement, each draw is independent of the others, and the probability of picking a purple marble is the same for each draw.

The number of purple marbles you pick on any given draw follows a binomial distribution with parameters n = 11 (the number of draws) and p = 7/11 (the probability of picking a purple marble on each draw). The expected value of a binomial distribution is given by n*p, so the best prediction for the number of times you will pick a purple marble is:

E(X) = np = 11(7/11) = 7

Therefore, the best prediction possible is that you will pick a purple marble approximately 7 times out of the 11 draws, on average. However, it's important to note that this is just a prediction based on probability, and the actual number of purple marbles you pick may vary from this expectation due to chance.

Answer 2

The best prediction possible for the number of times you will pick a purple marble can be found by calculating the expected value, which is the average number of times you would expect to pick a purple marble if you were to repeat this process many times.

The probability of selecting a purple marble on any given draw is 7/11, since there are 7 purple marbles out of 11 total marbles.

The expected value can be calculated by multiplying the probability of selecting a purple marble by the number of draws:

Expected value = probability of purple marble x number of draws
Expected value = (7/11) x 11
Expected value = 7

Therefore, the best prediction possible for the number of times you will pick a purple marble is 7.