Use the three different rules of calculating probabilities (conjunctions, negations, disjunctions) to calculate the following probabilities, which all related to fair, six-sided dice.

Question

1. What is the probability of rolling a five on one throw one die?
2. What is the probability of not rolling a five on one throw of one die?
3. What is the probability of rolling a five on your first throw and another five on the second throw of that die?
4. If you roll two dice at one time, what are the chances that both dice will come up twos?
5. If you roll two dice at one time, what are the chances that one or the other (or both) of the dice will come up a two?
6. If you roll two dice at once, what are the chances that at most one of the dice will come up a two?
7. If you roll two dice at once, what are the chances that at least one of the dice will come up a four?
8. If you roll two dice at once, what are the chances that there will be no fours?
9. If you roll two dice at once, what are the chances of rolling double fives?
10.If you roll two dice at once, what are the chances of rolling doubles (of any number)?

Answer 1

1. 1/6
2. 5/6
3. 1/36
4. 1/36
5. 12/36 or 1/3
6. 1/6 + 1/6 – 1/36 = 11/36
7. 2/6
8. 1 – 12/36 = 24/36 = 2/3
9. 1/36
10. 6/36