Your friend tell s you that she will stop by your house sometime after or equal to 1 p.m. and before 2 p.m., but she cannot give you any more information as her schedule is quite hectic. Your friend is very dependable, so you are sure that she will stop by your house, but other than that we have no information about the arrival time. Thus, we assume that the arrival time is completely random in the 1 p.m. and 2 p.m. interval. (As we will see, in the language of probability theory, we say that the arrival time is "uniformly" distributed on the [1, 2) interval). Let T be the arrival time.

a. What is the sample space S?

b. What is the probability of P(1.5)? Why?

c. What is the probability of T ∈ [1, 1.5)?

d. For 1 ≤ a ≤ b ≤ 2, what is P(a ≤ T ≤ b) = P([a, b])?