Question

A pair of fair dice each numbered 1 to 6 is tossed. Find the probability of a score of

a. Two odd numbers
b. A sum of 8 or sum of 12

Answer 1

In a pair of fair six-sided dice roll, the probability of scoring two odd numbers is 1/4, and the probability of rolling a sum of 8 or a sum of 12 is 1/6.

Step-by-step explanation:

When tossing a pair of fair six-sided dice, the sample space consists of 36 possible outcomes. For a pair of odd numbers, we consider the face values of {1, 3, 5} for each die, which creates the set {1, 3, 5} x {1, 3, 5}. There are 3 options on the first die and 3 on the second die, leading to 3 x 3 = 9 outcomes for two odd numbers.

For a sum of 8, possible outcomes are (2,6), (3,5), (4,4), (5,3), and (6,2), which consists of 5 outcomes. For a sum of 12, the only outcome is (6,6), giving us 1 outcome. To find the probability of each event, we divide the number of favorable outcomes by the total number of outcomes in the sample space (36). The probability of rolling two odd numbers is 9/36 or simplified to 1/4. The probability of rolling a sum of 8 is 5/36, and the probability of rolling a sum of 12 is 1/36. Adding the probabilities of a sum of 8 or 12, we get 5/36 + 1/36 = 6/36, which simplifies to 1/6.

Answer 2

1/4

1/6

Step-by-step explanation:

a) There is a 1/2 chance of rolling a odd number each time you roll it. Why? Because there are 3 odd numbers on a 6 sided die, 1,3,5. If we roll it twice, it would be 1/2 x 1/2 so a 1/4 chance

b) For it to be a sum of 8 the following combinations are possible, where the first number is rolled first and the second number is rolled second.

2,6

3,5

4,4

5,3

6,2

For it to be 12, it must be

6,6

There are a total of 6 ways to achieve this, and there is a total of 36 possible combinations, therefore 6/36 = 1/6 chance of rolling a sum of 8 or 12