Download Probability Exercise Sheet 1

Exercise Sheet Probability
Q1.
A sample of 1000 soccer supporters were asked for their opinion on who would
win next season’s Champions League. The results are summarised in the
following table:
Men
Women
Total
Man Utd
100
100
200
Barcelona Liverpool
170
130
130
50
300
180
Other Team
200
120
320
Total
600
400
1000
A supporter is chosen at random from the 1000.
What is the probability that the supporter:
(i)
(ii)
(iii)
(iv)
(v)
Q2.
thinks Liverpool will win
thinks Man Utd or Barcelona will win
is a man and thinks Liverpool will win
is a woman or thinks Man Utd will win
is a woman given the person chosen thinks Barcelona will win
One bag contains 4 white balls and 3 black balls. A second bag contains 2 white
balls and 5 black balls.
If one ball is drawn from each bag what is the probability that
(i) both are white
(ii) both are black
(iii) one is white and one is black
(iv) at least one is white
Q3.
A glass bottle manufacturer has three inspection points: one for size, the second
for colour and the third for flaws such as cracks and bubbles in the glass. The
probability that each inspection point will incorrectly accept or reject a bottle is
0.02. Calculate the following probabilities:
(a) A perfect bottle will be passed through all inspection points.
(b) A bottle faulty in colour and with a crack will be passed through all inspection
points.
(c) A bottle faulty in size only will be passed through all inspection points.
Q4.
A coin is tossed 3 times.
(a)
(b)
(c)
(d)
List all possible outcomes
What is the probability of no heads
What is the probability exactly 2 heads
What is the probability of at least 2 heads