Question

You roll a 6-sided die two times.What is the probability of rolling an odd number and then rolling a 1?Simplify your answer and write it as a fraction or whole number.

Answer 1

The events odd and prime are independent. The first roll does not affect the second roll.

Find P(odd). The die has 6 sides, numbered 1, 2, 3, 4, 5, and 6. The odd numbers are 1, 3, and 5. There are 3 odd numbers.

P(odd) =

3

6

Find P(prime). The prime numbers are 2, 3, and 5.

P(prime) =

3

6

Find the probability of rolling an odd number and then rolling a prime number. Multiply P(odd) by P(prime).

P(odd) x P(prime) =

3

6

×

3

6

=

9

36

Write your answer as a decimal. Then convert your answer to a percentage.

9

36

= 0.25 = 25%

The probability of rolling an odd number and then rolling a prime number is 25%.

Answer 2

The sample space for rolling a die twice is shown below

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 number of outcomes = 36

Outcomes involving an odd number followed by 1 = 1,1 3,1 5,1

Thus, number of favorable outcomes = 3

Probability = number of favorable outcomes/total number of outcomes

the probability of rolling an odd number and then rolling a 1 = 3/36

the probability of rolling an odd number and then rolling a 1 = 1/12