Question

On a single roll of two number cubes, what is the probability of rolling doubles given that the sum is 6

Answer 1

1/5

Explanation:

P(A/B)= P(A and B)/ P(B)

Sum of 6: 5/36

(1,5)---(5,1)---(2,4)---(4,2)---(3,3)

Probability of rolling doubles: 6/36

(1,1)---(2,2)---(3,3)---(4,4)---(5,5)---(6,6)

Out of these two "requirements" only one thing overlaps: (3,3)

Therefore:

P(A/B)= (1/36) ÷ (5/36)= 1/5

Answer 2

1/6

Explanation:

We can make a Punnett square to find number of favourable outcome

so

cube1

+

cube2 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

The probability of rolling doubles given that the sum is 6

favourable outcome / number of outcome

6 / 36

1 / 6