Grade 10 core mathematics – Probability I (12 lessons) Quiz
1. What is the probability of getting a head when a fair coin is tossed once?
A fair coin has two equally likely outcomes: head or tail. The probability of head is 1 out of 2, so 1/2.
2. A fair six-faced 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 six equally likely outcomes. So probability = 3/6 = 1/2.
3. A bag contains 3 red balls and 2 blue balls. One ball is drawn at random. What is the probability it is blue?
There are 2 blue balls out of a total of 3 + 2 = 5 balls, so probability = 2/5.
4. What is the sample space for tossing two coins once each?
Tossing two coins yields four equally likely ordered outcomes: both heads (HH), head then tail (HT), tail then head (TH), and both tails (TT).
5. A single fair die is rolled. What is the probability of getting a number greater than 4?
Numbers greater than 4 are 5 and 6 — two outcomes out of six. So probability = 2/6 = 1/3.
6. If the probability of an event A is 0.7, what is the probability of the complement A' (event A does not occur)?
Probability of an event and its complement add to 1. So A' = 1 − 0.7 = 0.3.
7. Two cards are drawn at random without replacement from a standard 52-card deck. What is the probability both are aces?
There are 4 aces. Probability first ace = 4/52, then without replacement probability second ace = 3/51. Multiply: (4/52)*(3/51) = 12/2652 = 1/221.
8. A fair coin is tossed three times. What is the probability of getting exactly two heads?
Number of sequences with exactly two heads is 3 (HHT, HTH, THH) out of 8 total outcomes, so probability = 3/8.
9. Which of the following statements is true about mutually exclusive events A and B?
Mutually exclusive (disjoint) events cannot occur together, so the probability they both happen is 0.
10. In an experiment, probability of rain today is 0.4 and probability of rain tomorrow is 0.5. If events are independent, what is the probability it rains both days?
For independent events multiply probabilities: 0.4 × 0.5 = 0.20.
11. A spinner is equally likely to stop at any of 8 numbered sections. What is the theoretical probability of landing on an odd number?
There are 4 odd numbers among 8 sections, so probability = 4/8 = 1/2.
12. A student performs an experiment and finds that event A occurred in 30 out of 120 trials. What is the experimental probability of A?
Experimental probability = frequency of A divided by total trials = 30/120 = 1/4.
13. You draw one ball from a bag containing 5 white and 5 black balls. You put the ball back and draw again. What is the probability both draws are white?
With replacement probabilities remain 5/10 = 1/2 each draw. Multiply: (1/2) × (1/2) = 1/4.
14. A fair six-faced die is rolled twice. What is the probability the sum is 7?
There are 6 favourable ordered outcomes that sum to 7 (1+6,2+5,3+4,4+3,5+2,6+1) out of 36 total, so 6/36 = 1/6.
15. If P(A) = 0.6 and A and B are mutually exclusive, what is the maximum possible value of P(B)?
Mutually exclusive events have P(A or B) ≤ 1, so P(B) ≤ 1 − P(A) = 0.4. Maximum possible is 0.4.
16. From a bag of 7 red and 3 green sweets, one sweet is drawn at random. What is the probability it is not red?
Not red means green. There are 3 green out of 10 total, so probability = 3/10.
17. Two dice are rolled. What is the probability of getting doubles (both dice show the same number)?
Doubles outcomes are (1,1),(2,2),...,(6,6) — 6 favourable out of 36 total, so 6/36 = 1/6.
18. A school has 3 boys and 2 girls on a committee. One student is chosen at random. What is the probability a girl is chosen?
There are 2 girls out of 5 students total, so probability = 2/5.
19. A single card is drawn from a well-shuffled deck of 52 cards. What is the probability the card is a heart?
There are 13 hearts in a 52-card deck, so probability = 13/52 = 1/4.
20. If the probability of event A is 0.25 and probability of event B is 0.4, what is the smallest possible value of P(A and B)?
The smallest possible overlap of two events is 0 when they are mutually exclusive, so P(A and B) can be 0.
21. A fair coin is tossed 4 times. How many possible equally likely outcomes are there?
Each toss has 2 outcomes, so total outcomes = 2^4 = 16.
22. From a box of 6 blue and 4 red pens, two pens are taken without replacement. What is the probability both are red?
First red = 4/10, then second red = 3/9. Multiply: (4/10)*(3/9) = 12/90 = 1/7.5 = 1/7.5 is 12/90 simplifies to 2/15? Correction: compute properly: (4/10)*(3/9)=12/90=2/15. But since 1/15 was listed, we must ensure correct option equals 2/15. Replace correct_choice with 2/15.
23. A week has seven days. If one day is chosen at random, what is the probability it is a weekend day (Saturday or Sunday)?
There are 2 weekend days out of 7 days, so probability = 2/7.
24. A bag contains 4 white and 6 black beads. One bead is drawn. Which event has higher probability: drawing a white bead or drawing a black bead?
There are 6 black and 4 white beads, so probability of black (6/10) is higher than white (4/10).
25. If two events are independent, which formula gives P(A and B)?
Independence means occurrence of one does not affect the other, so P(A and B) = P(A) × P(B).