Assume that 15% of the people in your expedition trip
own a mobile phone, and you are randomly assigned to
two partners in your group. Find the probability that:
a) The first partner will have a mobile phone.
b) The first partner will not have a mobile phone.
c) That both partners will have mobile phones.
d) That at most one will have a mobile phone.

Ottawa's Confederation Line trains arrive at peak times at a station
to a station on a Poisson basis, averaging 10 trains per hour.
1. What is the waiting time distribution of three trains? What is the
What is the probability that this waiting time is at most 25 minutes? What
What are the mean and variance of this random variable?
2. No train arrives during the first 5 minutes of waiting. What is the
What is the probability that there will be no train during the next 3 minutes?
3. What is the probability that two trains will arrive in twelve minutes?
4. At 95%, at least one train arrives in t-minutes. What is approximately
t in minutes?
5. A period of 5 minutes is said to be empty if it contains no arriving
of trains. What is the probability that at most one 5-minute period
is empty in one hour?

6. Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the mean and standard deviation of X are 11 gallons and 5 gallons, respectively.
(a) In a sample of 50 randomly selected customers, what is the approximate probability that the sample mean of the amount purchased X is at least 12 gallons? [Hint: use the central limit theorem]
(b) In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at least 600 gallons?

In examining borrower characteristics versus loan
delinquency, a bank has collected the following information:
(1) 15% of the borrowers who have been employed
at their present job for less than 3 years are behind in
their payments, (2) 5% of the borrowers who have been
employed at their present job for at least 3 years are
behind in their payments, and (3) 80% of the borrowers
have been employed at their present job for at least
3 years. Given this information:
a. What is the probability that a randomly selected
loan account will be for a person in the same job
for at least 3 years who is behind in making
payments?
b. What is the probability that a randomly selected loan
account will be for a person in the same job for less
than 3 years or who is behind in making payments?
c. If a loan account is behind, what is the probability
that the loan is for a person who has been in the
same job for less than 3 years?