Question

A bag contains 3 white marbles and 6 black marbles. You pick out a marble, record its color, and put the marble back in the bag. If you repeat this process 36 times, how many times would you expect to remove a black marble from the bag?

Answer 1

24 times you'd theoretically draw a black marble.
There is 9 marbles in the bag. Out of the 9, 6 are black so you have a $\frac{6}{9}$ chance to draw a black marble. $\frac{6}{9}$ multiplied my 36 is 24.(For this short cut, you multiply the favorable event's probability by the number of trials.)