Answer:
You expect to get 15 marbles.
Step-by-step 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:
[tex]E(X) = np[/tex]
There are 5+3+1 = 9 marbles.
Of those, 3 are white. So
[tex]p = \frac{3}{9} = \frac{1}{3}[/tex]
You repeat this process 45 times. How many white marbles do you expect to get ?
This is E(X) when n = 45. So
[tex]E(X) = np = 45*\frac{1}{3} = 15[/tex]
You expect to get 15 marbles.
