OpenCourseWare on critical thinking, logic, and creativity

Answers

1. The probability that the first die shows a 2 is 1/6.
2. The probability that the second die shows a 2 is 1/6.
3. The probability that both dice show a 2 is 1/61/6 = 1/36 (using the special multiplication rule, since the rolls are independent).
4. For the dice to add up to 4, there are three possibilities--either both dice show a 2, or the first shows a 3 and the second shows a 1, or the first shows a 1 and the second shows a 3. Each of these has a probability of 1/61/6 = 1/36 (using the special multiplication rule, since the rolls are independent). Hence the probability that the dice add up to 4 is 1/36 + 1/36 + 1/36 = 3/36 = 1/12 (using the special addition rule, since the outcomes are mutually exclusive).
5. If the first die shows a 2, then for the dice to add up to 4 the second die must also show a 2. So the probability that the dice add up to 4 given that the first shows a 2 is 1/6.
6. Note that we cannot use the simplified multiplication rule here, because the dice adding up to 4 is not independent of the first die showing a 2. So we need to use the full multiplication rule. This tells us that probability that the first die shows a 2 and the dice add up to 4 is given by the probability that the first die shows a 2, multiplied by the probability that the dice add up to 4 given that the first die shows a 2. This is 1/61/6 = 1/36.

• Return to main text.

---

Next: [Answers] Up: [Answers and stuff] Previous: [Answers]
Back to: [Frontpage]

<< previous page

---

---