Topic 10 Probability
Student assessment 1
1. There are 10 red, 6 blue and 8 green sweets in a packet.
a) If a sweet is picked at random, calculate the probability that it is:
i) red
ii) red or blue.
b) If the first sweet taken from the packet is blue and not put back,
calculate the probability that the second sweet is:
i) red
ii) blue or green.
2. A four-sided dice (numbered 1 to 4) and a six-sided dice
(numbered 1 to 6) are rolled and their scores added together.
a) Copy and complete the two-way table below showing all the
possible outcomes.
Six-sided dice
Four-sided dice
1
2
1
3
4
5
6
6
2
3
5
4
b) Calculate the probability of getting a total greater than 8.
c) Calculate the probability of getting a total score of 6.
3. A hexagonal spinner is split into sixths as shown (left).
The spinner is spun twice.
a) Draw a tree diagram to show all the possible outcomes.
b) Write the probability of each outcome on each branch.
c) Calculate the probability that the spinner lands on dark grey on
both occasions.
d) Calculate the probability that the spinner lands on dark grey at
least once out of the two spins.
4. A football team plays three matches. The team can either win,
draw or lose. The results of each match are independent of each
other. The probability of winning is 2–3 and the probability of
drawing is 1–4 .
a) Calculate the probability of losing.
b) Calculate the probability that the team wins all three matches.
c) Calculate the probability that the team does not lose all three
matches.
5. A student buys 15 tickets for a raffle. 300 tickets are sold in total.
Tickets for the two prizes are drawn at random. Calculate the
probability that:
a) the student wins both prizes
b) the student wins at least one prize.
Cambridge IGCSE International Mathematics © Hodder Education 2011
1
Topic 10 Probability: Student assessment 1
6. A college offers three sports clubs for its students to attend after
school. They are volleyball (V), basketball (B) and football (F).
The number of students attending each is shown in the Venn
diagram below.
V
B
20
30
U
5
10
25
15
55
40
F
a) How many students attend none of the sports clubs?
A student is picked at random. Calculate:
b) the probability that the student plays volleyball
c) P(V  B)
d) P(V  B  F)
e) P(V  F)
f) P(F ').
7.
A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}
B = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}
C = {5, 10, 15, 20, 25, 30}
a) Draw a Venn diagram showing the three sets of numbers.
b) A number is picked at random. Calculate:
i) P(A)
ii) P(B  C)
iii)P(A'  B).
8. In a class of 30 students, 24 study Biology, 14 study Chemistry and
1 studies neither.
a) Draw a Venn diagram to show this information.
b) A student is picked at random. Calculate:
i) P(B')
ii) P(B  C)
iii)P(B  C').
2
Cambridge IGCSE International Mathematics © Hodder Education 2011