Simulate the experiment described in Exercise 3.15, using any five identically shaped objects, two of which are one color and three another. Mix the objects, draw two, record the results, and then replace the objects. Repeat the experiment a large number of times (at least 100). Calculate the proportion of times events A, B, and C occur. How do these proportions compare with the probabilities you calculated in Exercise 3.15? Should these proportions equal the probabilities? Explain.

Exercise 3.15

Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles.

a. List the sample points.

b. Assign probabilities to the sample points.

c. Determine the probability of observing each of the following events:

A: {Two blue marbles are drawn.}

B: {A red and a blue marble are drawn.}

C: {Two red marbles are drawn.}