Nathan has 4 brown teddy bears. 5 pink teddy bears and 3 red teddy bears in his shop. Two teddy bears are drawn without replacement from the shop. What is the probability that both of the teddy bears are brown?

Question 7 Suppose that 5 independent trials, each of which results in any of the outcomes 0, 1, or 2, with respective probabilities 0.3, 0.5, and 0.2, are performed. Find the probability that both outcome 1 and outcome 2 occur at least once. (Hint: Consider the complementary probability.)

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?

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?