Question

The numbers 2, 3, 4, and 5 are indicated on cards that are placed in a hat.

Two cards are drawn at random, and the first card is replaced before the second card is drawn. The following table is a sample space of the possible outcomes.
Use the sample space of possible outcomes to determine the following probabilities.
1. Probability of drawing two odd numbers.
2. The sum of the two numbers drawn is less than 5.
3. The sum of the two numbers is less than 6 or greater than 8.

Answer 1

1. 1/4

2. 1/16

3. 3/8

Explanation:

1. 1/2 x 1/2, 1/4

2. (2,2) is the only way to have a sum less than 5, so 1/16

3. 3 ways to be less than 6 and 3 ways to be greater than 8, so 6/16 or 3/8

Answer 2

1. This probability is 1/2*1/2=1/4, or 0.25.
2. There are three ways to do this: draw two 2s, a three then a two, or a two then a three. So our probability is 3/16=.1875.
3. We already calculated the probability that the sum is less than 6. Using similar methods, we calculate that there are three ways for a sum to be greater than 8, so our probability is 6/16=0.375.