Question

A bag contains 10 red marbles, 7 blue marbles, and 3 green marbles. You randomly select a marble from the bag, record the color, and then put that marble back in the bag. If you were to do this 200 times, how many times would you expect to pull out a blue marble?

Answer 1

70

Explanation:

We have 7 blue marbles, and 20 total marbles. As a result, if we randomly chose one marble from the bag, the probability would be (number of favorable outcomes)/(number of total outcomes) = 7/20.

This means that for each 20 trials, we would expect to pull out a blue marble 7 times, as the probability does not change over time (because we put the marbles back, there are the same amount of each marble). Over 200 trials, we can simply make it out of 200 instead of 20. We can thus multiply 7/20 by 10/10 (10/10 is equal to 1, keeping the proportions equal) to get 70/200, so we can expect 70 blue marbles out of 200.