Question: (15 pts) You roll two fair dice.

a.) What is the sample space for this experiment?

b.) What is the probability that the first die is a 4?

c.) What is the probability that the sum is 6?

d.) What is the probability that the sum is 7?

e.) What is the probability that the sum is 6 or 7?

f.) What is the probability that the sum is 6 and 7?

g.) What is the probability that the first die is a 4 and the sum is 7?

h.) What is the probability that the first die is a 4 or the sum is 7?

i.) What is the probability that the sum is 7 given that the first die is a 4?

j.) Are the events “sum of 6” and “sum of 7” mutually exclusive? Why or why not?

k.) Are the events “sum of 7” and “first die is a 4” mutually exclusive? Why or why

not?

l.) Are the events “sum or 7” and “first die is a 4” independent? Why or why not?