Probability

11 Grade 9 Mathematics questions on Probability, with worked marking schemes. 11 questions are available on this topic in full.

1. Question 1

   4 marks

   A box has 4 white, 3 red, and 5 blue marbles. A marble is drawn at random. Find: (a) P(blue) (b) P(not white) (c) P(white or red)

   (4 marks)

   Marking scheme for this question

   Create a free account to see it

2. Question 2

   1 mark

   A coin is tossed twice. The sample space has ___ outcomes.

   A. 2

   B. 8

   C. 4

   D. 3

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

3. Question 3

   1 mark

   A bag contains $5$ red beads, $3$ blue beads and $4$ green beads. One bead is picked at random. What is the probability that it is green?

   A. $\frac{1}{4}$

   B. $\frac{1}{3}$

   C. $\frac{1}{2}$

   D. $\frac{1}{12}$

   (1 mark)

   Marking scheme

   B. $\frac{1}{3}$ — the bag holds $5+3+4=12$ beads, so $P(\text{green})=\frac{4}{12}=\frac{1}{3}$. D uses $1$ over the total instead of the number of green beads.

4. Question 4

   1 mark

   A class of 30 has 12 boys. A student is chosen at random. P(girl) = ___

   A. $\frac{2}{3}$

   B. $\frac{3}{5}$

   C. $\frac{12}{30}$

   D. $\frac{2}{5}$

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

5. Question 5

   1 mark

   The probability of an event that is certain is ___

   A. 1

   B. ∞

   C. 0

   D. 0.5

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

6. Question 6

   1 mark

   A die is thrown. What is the probability of getting an even number?

   A. $\frac{2}{3}$

   B. $\frac{1}{6}$

   C. $\frac{1}{3}$

   D. $\frac{1}{2}$

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

7. Question 7

   1 mark

   A bag has 3 red and 7 blue balls. The probability of picking a red ball is ___

   A. $\frac{7}{3}$

   B. $\frac{7}{10}$

   C. $\frac{3}{10}$

   D. $\frac{3}{7}$

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

8. Question 8

   4 marks

   A fair die is rolled. List the sample space and find the probability of getting: (a) a prime number (b) a number greater than 4.

   (4 marks)

   Marking scheme

   The sample space is every possible outcome: $S=\{1,2,3,4,5,6\}$, so $n(S)=6$. (1)

   (a) A prime number has exactly two factors, so the primes here are $\{2,3,5\}$ — note $1$ is not prime. (1)

   $P(\text{prime})=\frac{3}{6}=\frac{1}{2}$. (1)

   (b) Greater than $4$ means $\{5,6\}$, so $P=\frac{2}{6}=\frac{1}{3}$. (1)

   Final answer: (a) $\frac{1}{2}$ (b) $\frac{1}{3}$.

9. Question 9

   4 marks

   Two coins are tossed simultaneously. Find the probability of getting: (a) at least one head (b) exactly one tail.

   (4 marks)

   Marking scheme for this question

   Create a free account to see it

10. Question 10

    1 mark

    Two events are mutually exclusive if ___

    A. They cannot both occur at the same time

    B. One must occur

    C. They always occur together

    D. They have equal probabilities

    (1 mark)

    Marking scheme

    A. They cannot both occur at the same time — mutually exclusive means the events have no outcome in common, like a single die showing both a $2$ and a $5$.

11. Question 11

    1 mark

    If P(A) = 0.3, what is P(A')?

    A. 0.3

    B. 0.7

    C. 1.3

    D. 0

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

12. 8 more marking schemes are on this page. A free account opens all of them, and lets you build your own paper on the topics you have actually taught, laid out in KNEC format with its full marking scheme.

    Create a free account

More Grade 9 Mathematics topics