1MA01: Mathematical Methods Tutorial Sheet
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1. Determine if the following events are (a) independent and (b) disjoint.
(a) A coin is flipped twice. Let A be the event “the first flip is heads”
and B is the event “the second flip is tails”.
(b) A die is rolled Let A be the event “the die is a four” and B is the
event “the die is a five”.
2. Two tickets are drawn from the box containing 5 tickets labelled: 1, 2, 3, 4
and 5. The first ticket is not returned to the box before the second is
drawn. What is the probability of the events
(a) the first ticket is a 1?
(b) the first ticket is not a 2?
(c) the first ticket is a 2 or 3?
3. Consider rolling a (fair) die four times.
(a) what is the probability that all rolls are fives?
(b) what is the probability that the rolls are all the same?
(c) what is the probability that rolls are all different?
(d) what is the probability that a face (one side) appears more than
once?
4. Each student in a large class is given an identical box containing three
tickets marked 1, 2 and 3. Students are asked to draw two tickets from
the box without replacing the first.
(a) what proportion of students draw a 3 first?
(b) of the students that drew 3 first, what proportion draw a 1 second?
(c) what proportion of students in the class draw 3 first followed by 1?
5. Consider a five-day school week. The probability that it is Friday and
that a student is absent is 0.03. What is the probability that a student
is absent given that today is Friday?
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Sinéad Ryan, ryan@maths.tcd.ie, see also http://www.maths.tcd.ie/˜ryan/123.html