GRADE 9 Mathematics – PROBABILITY Quiz
1. A fair coin is tossed once. What is the probability of getting a head?
A fair coin has two equally likely outcomes (head or tail), so the probability of head is 1 out of 2, i.e. 1/2.
2. A single fair die is rolled. What is the probability of getting an even number?
Even faces on a die are 2, 4, 6 (three outcomes) out of 6 total, so probability = 3/6 = 1/2.
3. A fair die is rolled. What is the probability of getting a prime number?
Prime numbers on a die are 2, 3 and 5 (three outcomes) out of 6, so probability = 3/6 = 1/2.
4. Two fair dice are rolled. What is the probability that the sum of the two dice is 7?
There are 36 possible pairs; sums of 7 occur in 6 ways (1+6,2+5,3+4,4+3,5+2,6+1). So probability = 6/36 = 1/6.
5. One card is chosen at random from a standard 52-card deck. What is the probability that it is a heart?
There are 13 hearts in a 52-card deck, so probability = 13/52 = 1/4.
6. A bag contains 3 red, 2 blue and 5 green marbles. One marble is chosen at random. What is the probability it is blue?
Total marbles = 3+2+5 = 10. Probability of blue = 2/10 = 1/5.
7. From the bag with 3 red, 2 blue and 5 green marbles, two marbles are drawn one after the other without replacement. What is the probability both are red?
Probability first red = 3/10, then second red = 2/9. Multiply: (3/10)*(2/9) = 6/90 = 1/15.
8. From the same bag (3 red, 2 blue, 5 green), two marbles are drawn with replacement. What is the probability both are red?
With replacement the probability stays 3/10 each draw, so (3/10)*(3/10) = 9/100.
9. A spinner is divided into 4 equal sectors labelled A, B, C and D. What is the probability the spinner does not land on A?
Probability of A is 1/4, so not A is 1 - 1/4 = 3/4.
10. Two fair coins are tossed. What is the probability of getting at least one head?
Total outcomes: HH, HT, TH, TT. At least one head excludes TT only, so 3 out of 4 outcomes: 3/4.
11. A survey of 500 pupils shows 200 prefer mathematics. If one pupil is chosen at random, what is the experimental probability they prefer mathematics?
Experimental probability = number who prefer maths / total = 200/500 = 0.4.
12. One card is drawn from a 52-card deck. What is the probability that it is not a spade?
There are 13 spades, so not a spade = 39/52 = 3/4.
13. What is the expected value (mean) of a single fair die roll?
Expected value = (1+2+3+4+5+6)/6 = 21/6 = 3.5.
14. A bag has 2 red and 3 blue balls. One ball is drawn and it is red. Without returning it, what is the probability that the second ball drawn is red?
After removing one red, remaining are 1 red and 3 blue total 4, so probability = 1/4.
15. One card is drawn from a 52-card deck. What is the probability it is a king or a queen?
There are 4 kings and 4 queens, total 8 favorable cards, so 8/52 = 2/13.
16. A single card is drawn. What is the probability that the card is black or a heart?
Black cards = 26, hearts = 13, they do not overlap. So favourable = 26+13 = 39 out of 52 = 3/4.
17. In a class of 30 pupils there are 18 girls and 12 boys. If a pupil is chosen at random, what is the probability the pupil is a boy?
Probability = number of boys / total = 12/30 = 2/5.
18. Two coins are tossed. What is the probability that both show the same face?
Outcomes: HH, HT, TH, TT. Same face occurs for HH and TT (2 of 4), so probability = 2/4 = 1/2.
19. A fair die is rolled. What is the probability of getting a number less than 5?
Numbers less than 5 are 1,2,3,4 (4 outcomes) out of 6, so probability = 4/6 = 2/3.
20. If the probability of an event is 1/4, what are the odds in favour of the event?
Odds in favour = probability of event : probability of not event = (1/4) : (3/4) = 1:3.
21. A fair die is rolled three times. What is the probability of getting at least one six?
Probability of no six in one roll is 5/6; in three rolls (5/6)^3 = 125/216. So at least one six = 1 - 125/216 = 91/216.
22. Two cards are drawn from a 52-card deck without replacement. What is the probability both are aces?
Probability = (4/52)*(3/51) = 12/2652 = 1/221.
23. A fair coin is tossed and a die is rolled. What is the probability of getting a head on the coin and an even number on the die?
Events are independent. Probability head = 1/2, even on die = 1/2. Multiply: (1/2)*(1/2) = 1/4.
24. A box contains 2 red, 3 white and 5 black balls. One ball is drawn at random. What is the probability it is not black?
Not black means red or white: 2+3 = 5 favourable out of total 10, so probability = 5/10 = 1/2.