Question

1) Suppose you roll 2 dice. What is the probability that the sum of the 2 dice is ≤ 6, given that the 1st dice is a 1?

Express your answer as a fraction.

This is conditional probability I'm really having an issue understanding it.

Answer 1

Total number of outcomes = 36

Outcomes having sum less than or equal to 6 given that the 1st dice is 1

= {1,1}, {1,2}, {1,3}, {1,4}, {1,5}

Number of outcomes having sum less than or equal to 6 given that the 1st dice is 1 = 5

Probability that the sum of the 2 dice is ≤ 6, given that the 1st dice is a 1

= Number of outcomes having sum less than or equal to 6 given that the 1st dice is 1 / Total number of outcomes

= 5 / 36

Probability that the sum of the 2 dice is ≤ 6, given that the 1st dice is a 1 is 5/36