Question

Marcus placed 8 blue tiles and 12 red tiles in a container. He plans to draw a tile, record its color and replace it in the container before drawing another. If he does this 50 times, how many times should he expect to draw a red tile?

Answer 1

Let X be the number of times a red tile is drawn from the container      
Number of red tiles = 12      
Total tiles = 12 + 8 = 20      
p = P(randomly drawing a red tile) = 12/20 = 0.6      
n = 50 number of draws or trials     
Since Marcus replaces the tile before he draws the next tile, we can model      
the distribution of X according to Binomial Distribution      
Thus, X ~ Binomial with n = 50 and p = 0.6      
The Expected value of a binomial variable is E(X) = np      
E(X) = n * p      
         = 50 * 0.6      
         = 30      
Number of times Marcus should expect to draw a red tile = 30