6. A pair of dice are rolled once (so will have two numbers show up when we roll the pair). The {(1, 1), (1, 2), (1, 3), ., (6, 5), (6, 6)}. There are 36 elements in the sample space, and they are all equally likely to occur (thus each has probability of 36 of occurring). sample space is S .....

Suppose you roll a 6-sided die, a 10-sided die, and a 20-sided die. What is the probability that the roll on the 6-sided die is strictly larger than both of the other two dice?

If you roll SIX-6 sided dice, what is the probability that at least one of the dice has a three showing?

Suppose that you repeatedly roll a pair of fair dice and keep track of the sum. What is the probability that you see a sum of 7 before you see an even sum 3 times? (In particular, you keep track of how many evens you roll, and you want the probability that you roll a 7 before you get to 3 evens.

A gunball machine contains 5 red gumballs, 3 blue gumballs, and 4 yellow gumballs. You put a coin in the machine, and two gumballs come out one after the other. What is the probability that the first gumball that comes out is blue and the second gumboil is red?

Suppose that the prevalence of diabetes in the U.S. is 10% and that the prevalence of cardiovascular disease is 20%. Suppose also that 5% of people in the U.S. have both diabetes and cardiovascular disease.  Suppose Jack has diabetes. What is the probability that he also has cardiovascular disease?