• Part A: We throw two dice. Each one is a normal die with six equally-weighted sides. What is the probability that the sum of the two numbers is less than 7
Answer: Use the counting rule. When you roll two dice, there are 36 possible combinations for the two
numbers (N=36), all of them equally likely. Of these, 15 have a sum less than 7. So the probability is
Y /N = 15/36 ≈ 0.42.
• Part B: Suppose that the overall probability of living to age 70 is 0.62 and that the overall probability
of living to age 80 is 0.23. If a person reaches their 70th birthday, what is the probability that they will
live to age 80?
Answer: Use the multiplication rule for conditional probabilities: P(lives to 80 | lives to 70) = P(lives to 80,
lives to 70)/P(lives to 70). The joint probability isn’t explicitly given, so you have to recognize that P(lives
to 80, lives to 70) is the same as P(lives to 80), because in order to live to 80, you must have also lived to 70.
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