Six students (Dave, Michael, Ann, Joe, Jane, Bill) are attending a lecture in a class-
room with 10 seats. The seats are in a single row as follows
A B C D E F G H I J

All valid seating arrangements are equally likely. By valid seating arrangement we
mean that all students have to sit down in a seat and students can not share seats.
Here is an example of a valid seating arrangement:
Dave - B, Michael - A, Ann - E, Joe - I, Jane - H, Bill - F
(a) How many seating arrangements are there? Note that who sits where matters.
(b) What is the probability of the seating arrangement
Dave - A, Michael - C, Ann - D, Joe - H, Jane - I, Bill - J?
(c) What is the probability that Dave sits in seat A?
(d) What is the probability that seats A, C, D, H, I and J are occupied?
(e) What is the probability that seat A is occupied?
(f) What is the probability that Dave sits in A and Michael sits in C or Dave sits in
A and Bill sits in F?

2. We toss a fair six-sided die twice, and record the number that is showing on each toss.
(a) How many outcomes are there in the sample space?

(b) What is the probability that the die shows 5 at least once?

(c) What is the probability that the die does not show 5?

7 students randomly select one topic among A, B and C topics for a homework. What is the probabilitythat topic A is selected by exactly 2 students?

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?