Probability Questions From Past IB Exams
1. A bag contains 2 red balls, 3 blue balls and 4 green balls. A ball is chosen at random from
the bag and is not replaced. A second ball is chosen. Find the probability of choosing one
green ball and one blue ball in any order.
2. In a bilingual school there is a class of 21 pupils. In this class, 15 of the pupils speak Spanish
as their first language and 12 of these 15 pupils are Argentine. The other 6 pupils in the class
speak English as their first language and 3 of these 6 pupils are Argentine.
A pupil is selected at random from the class and is found to be Argentine. Find the
probability that the pupil speaks Spanish as his/her first language.
3. For the events A and B, p(A) = 0.6, p(B) = 0.8 and p(A ∪ B) = 1.
Find
(a) p(A∩B)
(b) p( A ∪ B)
4. A fair coin is tossed eight times. Calculate
(a) the probability of obtaining exactly 4 heads;
(b) the probability of obtaining exactly 3 heads;
(c) the probability of obtaining 3, 4 or 5 heads.
5. The local Football Association consists of ten teams. Team A has a 40 % chance of winning
any game against a higher-ranked team, and a 75 % chance of winning any game against a
lower-ranked team. If A is currently in fourth position, find the probability that A wins its
next game.
6. The following Venn diagram shows a sample space U and events A and B.
UA
B
n(U) = 36, n(A) = 11, n(B) = 6 and n(A ∪ B)’ = 21.
(a) On the diagram, shade the region (A ∪ B)’.
