TopicGeneral Maths
Statistics & probability · SS2–SS3
Probability
How likely events are, including combined events, “and” and “or”, and tree diagrams.
Learn
- 1Probability and sample spacesProbability as favourable outcomes over possible outcomes: listing sample spaces, using tables of results, the complement, and 'or' with and without overlap.Done16 min
- 2Combined events and tree diagramsTwo or more events together: multiply for 'and', add for 'or', tree diagrams, draws with and without replacement, and 'at least one' by the complement.Done18 min
Practise
Answer probability questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
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Past questions (129)
From 1983–2025: 64 WAEC, 12 NECO, 53 JAMB. Theory questions first, then objective, newest first.
Theory (50)
- WAEC 2025 · Paper 2 · Q4A pack of 52 playing cards is shuffled and one card is drawn. Find the probability that it is either a five or a red nine.
- WAEC 2024 · Paper 2 · Q5A basket contains 3 gold-plated marbles, 4 diamond marbles and some silver marbles, all of the same size and shape. Two marbles were drawn from …
- NECO 2023 · Paper 2 · Q5In a certain school, the principal gave the analysis of the qualified subject teachers as follows.
- WAEC 2023 · Paper 2 · Q6, where is a counting number. Write down all the elements in .
- WAEC 2023 · Paper 2 · Q12In the diagram, , , and . …
- NECO 2022 · Paper 2 · Q12The pie chart below shows the sectorial allocation of subjects offered by 720 students in a college.
- WAEC 2022 · Paper 2 · Q12The probability that an athlete will not win any of the three races is . If the athlete runs in all the races, what is the probability …
- WAEC 2022 · Paper 2 · Q5Given that and , simplify, without using a calculator, , leaving the answer in the form …
- WAEC 2022 · Paper 2 · Q5A bird perches on the top of a slanted tree of length . If the bird is vertically above the ground, (i) illustrate …
- WAEC 2022 · Paper 2 · Q8In a class of 60 students, 30 read Literature and 35 read Government. All the students read at least one of the subjects. If a student is …
- WAEC 2022 · Paper 2 · Q11| Marks | 2 | 3 | 4 | 5 | 6 |
- WAEC 2022 · Paper 2 · Q9In a class of 50 students, 18 play football, 20 volleyball and 21 handball. 9 play football and volleyball, 6 football and handball, 11 volleyball …
- WAEC 2021 · Paper 2 · Q5| Child's name | Ann | Afia | Kojo | Nuno | Akosua |
- WAEC 2021 · Paper 2 · Q13There are 20 men on a public bus. Of these, 15 wear glasses and 10 wear wrist watches. If one man is chosen at random from the bus, what is the …
- WAEC 2021 · Paper 2 · Q5There are 25 boys and 15 girls in a class, all of them equally likely to be chosen for a contest. If two students are chosen one after the other …
- WAEC 2020 · Paper 2 · Q5| Number | 1 | 2 | 3 | 4 | 5 | 6 |
- WAEC 2020 · Paper 2 · Q2Given that and , evaluate .
- WAEC 2020 · Paper 2 · Q9Differentiate .
- WAEC 2020 · Paper 2 · Q12In the diagram, , , , , , lie on a straight line and . Find the value …
- WAEC 2020 · Paper 2 · Q5A number is selected at random from the set . Find the probability that the number selected is:
- WAEC 2019 · Paper 2 · Q5Three red balls, five green balls and a number of blue balls are put together in a sack. One ball is picked at random from the sack. If the probability …
- WAEC 2019 · Paper 2 · Q9A survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study …
- WAEC 2019 · Paper 2 · Q13In the diagram, , , , are points on the circle with centre . and . Find: (i) …
- WAEC 2019 · Paper 2 · Q3Without using mathematical tables or calculators, simplify .
- WAEC 2018 · Paper 2 · Q9| Marks (%) | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 |
- WAEC 2017 · Paper 2 · Q5Out of 120 customers in a shop, 45 bought bags and shoes. All the customers bought either bags or shoes, and 11 more customers bought shoes than …
- WAEC 2017 · Paper 2 · Q8| Marks | 1 | 2 | 3 | 4 | 5 |
- WAEC 2017 · Paper 2 · Q11Sets and are subsets of . If a number is selected …
- WAEC 2017 · Paper 2 · Q5| Marks | 40 | 41 | 42 | 43 | 44 | 45 | 46 |
- WAEC 2017 · Paper 2 · Q8The probabilities that Akafi and Iniola will pass an examination are and respectively. Find the probability that only Iniola …
- WAEC 2016 · Paper 2 · Q4| Score | 1 | 2 | 3 | 4 | 5 | 6 |
- WAEC 2016 · Paper 2 · Q2If , make the subject of the equation.
- WAEC 2015 · Paper 2 · Q1Without using mathematical tables or a calculator, simplify .
- WAEC 2015 · Paper 2 · Q13| Marks (%) | 0–9 | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 |
- WAEC 2014 · Paper 2 · Q11| Score | 1 | 2 | 3 | 4 | 5 | 6 |
- WAEC 2014 · Paper 2 · Q5A building contractor tendered for two independent contracts, and . The probability that he will win contract is and that he …
- WAEC 2014 · Paper 2 · Q11The probabilities that Manful, John and Ernest will pass an examination are , and respectively. Find the probability …
- WAEC 2013 · Paper 2 · Q11| Marks (%) | 1–10 | 11–20 | 21–30 | 31–40 | 41–50 | 51–60 | 61–70 | 71–80 | 81–90 | 91–100 |
- WAEC 2012 · Paper 2 · Q4A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is , calculate the number …
- WAEC 2012 · Paper 2 · Q2Given that , and , find: (i) ; (ii) .
- WAEC 2012 · Paper 2 · Q6Simplify: .
- WAEC 2011 · Paper 2 · Q11| Score | 1 | 2 | 3 | 4 | 5 | 6 |
- WAEC 2011 · Paper 2 · Q6In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 Mathematics and Accounts only, 6 Mathematics only, …
- WAEC 2010 · Paper 2 · Q12The frequency distribution of the weight of 100 participants in a high jump competition is as shown below.
- WAEC 2010 · Paper 2 · Q5Write out the elements of and .
- WAEC 2010 · Paper 2 · Q1Two children shared an amount of money in the ratio . If the smaller share was GH¢25.00, how much was shared between them?
- WAEC 2009 · Paper 2 · Q3The table shows the number of children per family in a community.
- WAEC 2009 · Paper 2 · Q3The probability that a malaria patient survives when given a newly discovered drug is , and the probability that a typhoid patient …
- WAEC 2009 · Paper 2 · Q7The marks scored by 50 students in a Geography examination are as follows:
- WAEC 2008 · Paper 2 · Q10In a class of 200 students, 70 offered Physics, 90 Chemistry and 100 Mathematics, while 24 did not offer any of the three subjects. Twenty-three …
Objective (79)
- WAEC 2025 · Paper 1 · Q48Two fair dice are tossed once. Find the probability that the sum is at least 10.
- WAEC 2025 · Paper 1 · Q50A box contains 2 red, 6 white and 5 black balls. A ball is selected at random. What is the probability that it is black?
- NECO 2024 · Paper 1 · Q54Tickets numbered 1 to 16 inclusive are mixed up and a ticket is drawn at random. What is the probability that the number is a multiple of 2 or …
- NECO 2024 · Paper 1 · Q55The lucky numbers in a raffle draw are 4, 5, 12, 20, 2, 8, 3, 6, 10, 9, 7, 25, 12, 10, 14, 27. If a number is picked at random, what is the probability …
- NECO 2024 · Paper 1 · Q56The probabilities that it will rain in Lagos and Oyo on the same day are and respectively. Find the probability that it will …
- NECO 2024 · Paper 1 · Q57The table shows the ages of students in a class. What is the probability that a student chosen at random is less than 18 years old?
- WAEC 2024 · Paper 1 · Q42A die is tossed once. Find the probability of getting a prime number.
- WAEC 2024 · Paper 1 · Q46The probability that Amaka will pass an examination is and that Bala will pass is . Find the probability that both will pass …
- NECO 2023 · Paper 1 · Q50What is the probability that an integer selected from is a prime number?
- NECO 2023 · Paper 1 · Q51Two balls are taken one after the other without replacement from a bag containing 4 red and 6 blue balls. What is the probability that they are …
- NECO 2023 · Paper 1 · Q55The table shows the scores of applicants in an interview. If an applicant is chosen at random, what is the probability that the applicant scored …
- NECO 2023 · Paper 1 · Q56A box contains 20 oranges, 14 of them ripe and 6 unripe. If two oranges are taken one after the other with replacement, find the probability …
- WAEC 2023 · Paper 1 · Q32A bag contains 4 white marbles and 3 blue marbles. Another bag contains 5 red marbles and 6 blue marbles. If a marble is picked at random from …
- WAEC 2023 · Paper 1 · Q41A number is chosen at random from 40 to 50 inclusive. Find the probability that the number is prime.
- WAEC 2023 · Paper 1 · Q42The bar chart represents the distribution of marks scored by students in an economics examination. If the fail mark was 4, what is the probability …
- NECO 2022 · Paper 1 · Q54Two fair dice are thrown together. Calculate the probability that the sum obtained is less than 8.
- NECO 2022 · Paper 1 · Q55Two fair dice are thrown together. Find the probability that the sum obtained is a multiple of 6.
- WAEC 2022 · Paper 1 · Q32Mrs Gabriel is pregnant. The probability that she will give birth to a girl is and the probability that the baby will have blue eyes …
- WAEC 2022 · Paper 1 · Q43A local community has two newspapers, the Morning Times and the Evening Dispatch. The Morning Times is read by of the households and the …
- WAEC 2021 · Paper 1 · Q45A box contains 40 identical balls of which 10 are red and 12 are blue. A ball is selected at random. What is the probability that it is neither …
- WAEC 2021 · Paper 1 · Q46A fair die is tossed twice. What is the probability of getting a sum of at least 10?
- WAEC 2020 · Paper 1 · Q39A box contains 12 identical balls of which 5 are red, 4 blue and the rest green. If a ball is selected at random, what is the probability that …
- WAEC 2020 · Paper 1 · Q40A box contains 12 identical balls of which 5 are red, 4 blue and the rest green. If two balls are selected at random one after the other with …
- WAEC 2019 · Paper 1 · Q18There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
- WAEC 2019 · Paper 1 · Q33A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what …
- WAEC 2019 · Paper 1 · Q45A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?
- JAMB 2017 · UTME · Q15A container has 30 gold medals, 22 silver medals and 18 bronze medals. If one medal is selected at random, what is the probability that it is …
- JAMB 2017 · UTME · Q20What is the probability that an integer , , chosen at random is divisible by both 2 and 3?
- JAMB 2017 · UTME · Q34Teams and are involved in a game of football. What is the probability that the game ends in a draw?
- JAMB 2017 · UTME · Q40In a class of 60 students, 30 offer physics and 40 offer chemistry. If a student is picked at random from the class, what is the probability …
- JAMB 2017 · UTME (set 2) · Q3If , and , …
- JAMB 2016 · UTME · Q8A crate of soft drinks contains 10 bottles of Coca-Cola, 8 of Fanta and 6 of Sprite. If one bottle is selected at random, what is the probability …
- JAMB 2014 · UTME · Q49| Number | 1 | 2 | 3 | 4 | 5 | 6 |
- JAMB 2014 · UTME · Q50A number is chosen at random from 10 to 30, both inclusive. What is the probability that the number is divisible by 3?
- JAMB 2013 · UTME · Q49What is the probability that an integer () chosen at random is divisible by both 2 and 3?
- JAMB 2013 · UTME · Q50A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket. Find the probability that it is neither an apple nor …
- JAMB 2012 · UTME · Q49The probability that a student passes a physics test is . If he takes three physics tests, what is the probability that he passes two …
- JAMB 2012 · UTME · Q50The probabilities that a man and his wife live to 80 years are and respectively. Find the probability that at least one of …
- JAMB 2011 · UTME · Q49Find the probability that a number picked at random from the set is a prime number.
- JAMB 2011 · UTME · Q50In a class of 60 students, 30 offer Physics and 40 offer Chemistry. If a student is picked at random from the class, what is the probability …
- JAMB 2010 · UTME · Q50If three unbiased coins are tossed, find the probability that they are all heads.
- JAMB 2004 · UME · Q48Some white balls were put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white ball from the …
- JAMB 2004 · UME · Q50A container has 30 gold medals, 22 silver medals and 18 bronze medals. If one medal is selected at random, what is the probability that it is …
- JAMB 2003 · UME · Q43A bag contains 5 black balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and a …
- JAMB 2003 · UME · Q48Two dice are thrown. What is the probability that the sum of the numbers is divisible by 3?
- JAMB 2002 · UME · Q25In a class of 80 students, offer Music only, offer both Music and History, offer History only and 20 offer neither. If …
- JAMB 2002 · UME · Q27The probability of a student passing any examination is . If the student takes three examinations, what is the probability that he will …
- JAMB 2001 · UME · Q40The bar chart shows the colours of cars passing a point on a street in two minutes. What fraction of the total number of cars is yellow?
- JAMB 2001 · UME · Q49The distribution of colours of beads in a bowl is: blue 1, black 2, yellow 4, white 5, brown 3. What is the probability that a bead selected …
- JAMB 2001 · UME · Q50Teams and are involved in a game of football. What is the probability that the game ends in a draw?
- JAMB 2000 · UME · Q41 and are two events. The probability of or is 0.7 and the probability of is 0.4. If and are independent, find the …
- JAMB 2000 · UME · Q45If , and , …
- JAMB 1999 · UME · Q41Three boys play a game of luck in which their respective chances of winning are , and . What is the probability that …
- JAMB 1999 · UME · Q42A number is selected at random from 0 to 20. What is the probability that the number is an odd prime?
- JAMB 1998 · UME · Q46A bag contains 16 red balls and 20 blue balls only. How many white balls must be added to the bag so that the probability of randomly picking …
- JAMB 1998 · UME · Q49In a recent zonal championship involving 10 teams, teams and were given probabilities and respectively of winning …
- JAMB 1998 · UME · Q50If and can take values from the set , find the probability that the product of and is not greater than 6.
- JAMB 1997 · UME · Q49In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that it is either …
- JAMB 1997 · UME · Q50A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is even.
- JAMB 1995 · UME · Q50A die has four of its faces coloured white and the remaining two coloured black. What is the probability that when the die is thrown two consecutive …
- JAMB 1994 · UME · Q49The table shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years …
- JAMB 1994 · UME · Q50In a survey, 20 students read newspapers and 35 read novels. If 40 of the students read either newspapers or novels, what is the probability …
- JAMB 1993 · UME · Q48A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime.
- JAMB 1993 · UME · Q50The chances of three independent events , and occurring are , and respectively. What is the chance of …
- JAMB 1992 · UME · Q47Two fair dice are thrown together. Determine the probability of obtaining a total score of 8.
- JAMB 1992 · UME · Q48The probability of an event is while that of another event is . If the probability of both and is , …
- JAMB 1991 · UME · Q50A crate of soft drinks contains 10 bottles of Coca-Cola, 8 of Fanta and 6 of Sprite. If one bottle is selected at random, what is the probability …
- JAMB 1990 · UME · Q49Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?
- JAMB 1989 · UME · Q50Two numbers are chosen at random from the three numbers 1, 3, 6. Find the probability that the sum of the two is not odd.
- JAMB 1988 · UME · Q50If two dice are thrown together, what is the probability of obtaining a score of at least 10?
- JAMB 1987 · UME · Q50Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium.
- JAMB 1986 · UME · Q47Find the probability that a number selected at random from 40 to 50 is a prime.
- JAMB 1986 · UME · Q49A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?
- JAMB 1985 · UME · Q30If two fair coins are tossed, what is the probability of getting at least one head?
- JAMB 1985 · UME · Q35What is the probability that a number chosen at random from the integers 1 to 10 inclusive is either a prime or a multiple of 3?
- JAMB 1985 · UME · Q44A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both …
- JAMB 1984 · UME · Q40Two fair dice are rolled. What is the probability that both show the same number?
- JAMB 1984 · UME · Q9Bola chooses at random a number from 1 to 300. What is the probability that the number is divisible by 4?
- JAMB 1983 · UME · Q29The letters of the word MATRICULATION are cut and put into a box. One letter is drawn at random. Find the probability of drawing a vowel.