Two ordinary fair, six-sided dice are rolled. What is the probability the sum of

Question

Two ordinary fair, six-sided dice are rolled.

What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 3?  

What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 3?  

What is the probability the sum of the numbers on the two dice is 9, given that it is not 3?  

What is the probability exactly one of the dice shows the number 1 given that the sum of the numbers is 6?  

Enter your answers as whole numbers or factions in lowest terms.

Explanation / Answer

E -> Event and P(E) -> Probability of Event.

a) E = {3,3}

P(E) = 1/36

b) E = {3,5}, {5,3}

P(E) = 2/36 = 1/18

c) E = {2,7}, {7,2}, {4, 5}, {5, 4}

P(E) = 4/36 = 1/9

d) E = {1,5}, {5,1}

P(E) = 2/36 = 1/18

in each curly bracket first element shows the outcome of first die and 2nd element shows the outcome of second die when both dice rolled simultaneously.

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