Find the probability for the experiment of tossing a six-sided die twice.

1. The sum is 4.

2. The sum is 6.

3. The sum is at least 7.

4. The sum is at least 8.

5. The sum is less than 11.

6. The sum is 2, 3, or 12.

7. The sum is odd and no more than 7.

8. The sum is odd or prime.

1. 1/12 or 0.083

2. 5/36 or 0.1389

3. 7/12 or 0.5833

4. 5/12 or 0.4167

5. 11/12 or 0.9167

6. 1/9 or 0.1111

7. 1/3 or 0.3333

8. 5/12 or 0.4167

Step-by-step explanation:

This problem can easily be understood by making sample space first.

Outcomes in sample space=S={ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

Total outcomes=36

The probability in the following scenario is calculated as

Probability=number of outcomes/Total outcomes

1.

The sum is 4

The sum is 4 = { (1,3), (2,2), (3,1) }

number of outcomes=3

P (The sum is 4) = 3/36=1/12 or 0.083

2.

The sum is 6

The sum is 6 = { (1,5), (2,4), (3,3), (4,2), (5,1) }

number of outcomes=5

P (The sum is 6) = 5/36 or 0.1389

3.

The sum is at least 7

The sum is at least 7=The sum is greater than or equal to 7

The sum is at least 7={ (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

number of outcomes=21

P (The sum is at least 7) = 21/36

P (The sum is at least 7) = 7/12 or 0.5833

4.

The sum is at least 8

The sum is at least 8=The sum is greater than or equal to 8

The sum is at least 8={ (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6) }

number of outcomes=15

P (The sum is at least 8) = 15/36

P (The sum is at least 8) = 5/12 or 0.4167

5.

The sum is less than 11

The sum is less than 11={ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (6,1), (6,2), (6,3), (6,4) }

number of outcomes=33

P (The sum is less than 11) = 33/36

P (The sum is less than 11) = 11/12 or 0.9167

6.

The sum is 2, 3, or 12

The sum is 2, 3, or 12={ (1,1), (1,2), (2,1), (6,6) }

number of outcomes=4

P (The sum is 2, 3, or 12) = 4/36

P (The sum is 2, 3, or 12) = 1/9 or 0.1111

7.

The sum is odd and no more than 7

The sum is odd and no more than 7={ (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,2), (6,1) }

number of outcomes=12

P (The sum is odd and no more than 7) = 12/36

P (The sum is odd and no more than 7) = 1/3 or 0.3333

8.

The sum is odd or prime

The sum is odd or prime={ (1,1), (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,2), (5,6), (6,1), (6,5) }

number of outcomes=15

P (The sum is odd or prime) = 15/36

P (The sum is odd or prime) = 5/12 or 0.4167