A long-distance taxi service company owns three vehicles. These vehicles are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.90, 0.80, and 0.85. Whether one vehicle is available is independent of whether any other vehicle is available. a) Find the probability distribution for the number of vehicles available for use on a given day. (Hint: define a random variable X as the number of vehicles available for use on a given day. Now, figure out how many different values it can assume and what are the corresponding probabilities?) b) Find the expected number of vehicles available for use on a given day. c) Find the standard deviation of the number of vehicles available for use on a given day.

a) Which of the following statements are true? (a and b are integers.) Give informal ex- planations of your answers. i) If a and b are even, then ab is even. ii) If a and b are odd, then ab is odd. iii) If ab is odd, then a and b are both odd. iv) If ab is even, then a and b are both even. b) Formulate correct principles, similar in style to those of part i), for dealing with sums of odd and even integers.

1. Complete the statement: In the diagram at the right. AB is? to CC, and point B is the ?