Grade 10 essential mathematics โ Probability I Quiz
1. A fair coin is tossed once. What is the probability of getting heads?
A fair coin has two equally likely outcomes, heads or tails, so the probability of heads is 1 out of 2, i.e. 1/2.
2. A fair six-sided die is rolled. What is the probability of getting an even number?
Even numbers on a die are 2, 4 and 6 โ three outcomes out of six total, so probability = 3/6 = 1/2.
3. A bag contains 5 red, 3 blue and 2 green marbles. If one marble is taken at random, what is the probability it is green?
There are 2 green marbles out of a total of 5+3+2 = 10, so probability = 2/10 which can be simplified to 1/5.
4. Two fair coins are tossed. What is the probability of getting two heads?
There are 4 equally likely outcomes (HH, HT, TH, TT). Only HH is two heads, so probability = 1/4.
5. A fair die is rolled. What is the probability of NOT getting a 6?
There is one outcome that is a 6, so the probability of not getting 6 is the remaining 5 outcomes out of 6 = 5/6.
6. A student performed an experiment 20 times and got the event success 7 times. What is the experimental probability of success?
Experimental probability = number of successes divided by total trials = 7 รท 20 = 7/20.
7. If the weather forecast says a 0.3 chance of rain, what is this probability as a percentage?
To convert a decimal to a percent multiply by 100: 0.3 ร 100 = 30%.
8. From a standard 52-card deck, what is the probability of drawing either a king or a queen?
There are 4 kings and 4 queens, total 8 favourable cards out of 52. So probability = 8/52 = 2/13.
9. A fair spinner has 8 equal sectors numbered 1 to 8. What is the probability it lands on a number divisible by 4?
Numbers divisible by 4 are 4 and 8 โ 2 favourable outcomes out of 8 sectors, so 2/8 = 1/4.
10. A bag has 4 red and 6 black marbles. Two marbles are drawn without replacement. What is the probability both are red?
Probability first red = 4/10. Then without replacement, probability second red = 3/9. Multiply: (4/10)ร(3/9)=12/90=2/15.
11. A bag has 4 red and 6 black marbles. You draw a marble, replace it, then draw again. What is the probability both draws are red?
With replacement probabilities remain same: (4/10)ร(4/10) = (2/5)ร(2/5) = 4/25.
12. Two fair coins are tossed. What is the probability of getting at least one head?
Only outcome with no heads is TT (1 out of 4). So probability at least one head = 1 โ 1/4 = 3/4.
13. In a class of 50 students, 15 scored above 80 marks. If one student is chosen at random, what is the probability they scored above 80?
Probability = favourable รท total = 15/50 = 3/10.
14. A fair six-sided die is rolled. What is the probability of getting a prime number?
Prime numbers on a die are 2, 3 and 5 โ 3 out of 6 outcomes, so probability = 3/6 = 1/2.
15. From a standard 52-card deck, what is the probability of NOT drawing an ace?
There are 4 aces so 48 non-aces. Probability = 48/52 = 12/13.
16. A letter is chosen at random from the word 'KENYA'. What is the probability the letter is a vowel?
Letters in KENYA: K, E, N, Y, A. Vowels are E and A = 2 out of 5, so probability = 2/5.
17. In a class of 20 students, 6 wear shoe size 7, 8 wear size 6 and 6 wear size 5. If a student is chosen at random, what is the probability they wear size 6?
There are 8 students with size 6 out of 20 total, so probability = 8/20 = 2/5.
18. A fair spinner has 10 equal sections numbered 1 to 10. What is the probability it lands on a number less than 6?
Numbers less than 6 are 1,2,3,4,5 โ five favourable out of 10, so probability = 5/10 = 1/2.
19. Two fair dice are rolled. What is the probability their sum is 7?
There are 6 favourable outcomes giving sum 7 out of 36 total possible pairs, so probability = 6/36 = 1/6.
20. From a standard 52-card deck, what is the probability of drawing a red card?
Half the deck is red (hearts and diamonds) so 26 out of 52 cards are red; probability = 26/52 = 1/2.
21. A raffle has tickets numbered 1 to 100. One ticket is drawn at random. What is the probability the number is divisible by 5?
Numbers divisible by 5 from 1 to 100 are 5,10,...,100 โ there are 20 such numbers. Probability = 20/100 = 1/5.
22. Two fair dice are rolled. What is the probability of getting at least one six?
Probability of no six on a roll is 5/6. For two rolls: (5/6)^2 = 25/36. So at least one six = 1 โ 25/36 = 11/36.
23. A fair six-sided die is rolled. What is the probability of getting an odd number?
Odd faces are 1, 3 and 5 โ three favourable outcomes out of six, so probability = 3/6 = 1/2.
24. A spinner is divided into 6 equal sectors: 3 red, 2 blue and 1 green. What is the probability it lands on blue?
Blue has 2 sectors out of 6, so probability = 2/6 = 1/3.
25. A jar has 12 biscuits: 5 chocolate and 7 plain. One biscuit is chosen at random. What is the probability it is chocolate?
Favourable outcomes are 5 chocolate biscuits out of 12 total, so probability = 5/12.