Probability is an important topic, and students should be able to test theoretical computations against experimental data.

Consider a deck of 52 cards with the following characteristics:

13 red cards, numbered 1 through 13

13 blue cards, numbered 1 through 13

13 green cards, numbered 1 through 13

13 black cards, numbered 1 through 13

Task:

A. Determine the theoretical and experimental probabilities:

1. Describe the steps necessary to calculate the theoretical probability of:

a. Drawing two red cards one after the other from the given deck if the cards are returned to the deck after each pick.

b. Drawing three cards with the same value one after the other from the given deck without replacing them in the deck after each pick.

2. Describe the steps necessary to calculate the experimental probabilities of:

a. Drawing two red cards one after the other from the given deck if the cards are returned to the deck after each pick.

b. Drawing three cards with the same value one after the other from the given deck without replacing them in the deck after each pick.