BU7527
Example sheet — 1
Mike Peardon — mjp@maths.tcd.ie
School of Mathematics, TCD
Monday, 28th September
Try to answer these questions before tomorrow’s lectures. We will go through solutions
in class.
1. Two dice are rolled. What is the probability the biggest number showing on either of
the dice was more than four given the smallest number was more than two?
2. A group of friends, three men and six women are going out and call a taxi. A random
selection of four friends get into the taxi. Find the probability the taxi contains
1. Two men and two women.
2. Four women.
3. At least two men.
3. In a game, a player takes turns to roll a die and keeps a count of N , the number of
turns taken. If the number showing is less than or equal to N , the game stops. Find
P (N = n) at the end of the game for all possible values of n.
4. Two fair dice are rolled. If we define two events A and B such that A is said to have
occurred if the first roll is a six and B is said to have occured if the sum of the two
rolls is seven then are A and B independent? What if the sum of the rolls is ten?
5. Bayes theorem: The probability your friend finds a mathematics lecture interesting
is 95% and mathematics lectures make up 10% of their modules this semester. The
probability they find a lecture for any other course interesting is 5%. You overhead
your friend saying they have just enjoyed an interesting lecture. What is the probability
they have just attended a mathematics lecture?
6. Binomial experiment: To improve profits, the airline BinomialAir sells more tickets
for each flight than there are seats on its planes. Each plane has 20 seats and the
airline always sells 24 tickets. On average, 19 passengers actually check in. What
is the probability that on a particular flight, more passengers check in than can be
accommodated on the plane?
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