Question

A bag contains 5 red marbles, 3 white marbles and 1 grey marble. You randomly pick out a marble, record its color and put it back in bag. You repeat this process 45 times. How many white marbles do you expect to get ?

Answer 1

You expect to get 15 marbles.

Explanation:

Since the marble is put back in the bag, in each trial, the probability of getting a white marble is the same.

Also, there are only two possible outcomes. Either we pick a white marble, of we do not. The probability of getting a white marble on a trial is independent of other trials. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

There are 5+3+1 = 9 marbles.

Of those, 3 are white. So

`p = (3)/(9) = (1)/(3)`

You repeat this process 45 times. How many white marbles do you expect to get ?

This is E(X) when n = 45. So

`E(X) = np = 45*(1)/(3) = 15`

You expect to get 15 marbles.