Probability

13 Grade 8 Mathematics questions on Probability, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   1 mark

   What is the probability of an impossible event?

   A. 1

   B. 0

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

   D. 100

   (1 mark)

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2. Question 2

   1 mark

   A fair coin is tossed once. What is the probability of getting a head?

   A. 1

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

   C. 2

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

   (1 mark)

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3. Question 3

   3 marks

   A box contains 5 red, 3 blue and 2 white pens. One pen is picked at random.

   (a) Find the probability that it is blue. (1 mark)

   (b) Find the probability that it is not white. (2 marks)

   Marking scheme

   Probability is $\frac{\text{favourable outcomes}}{\text{total outcomes}}$. The box holds $5+3+2=10$ pens in all. (1)

   (a) Three of the ten are blue, so $P(\text{blue})=\frac{3}{10}$. (1)

   (b) "Not white" covers the $5$ red and $3$ blue, that is $8$ pens: $P=\frac{8}{10}=\frac{4}{5}$. (1)

   Final answer: (a) $\frac{3}{10}$ (b) $\frac{4}{5}$.

4. Question 4

   1 mark

   A bag contains 3 red and 2 blue balls. A ball is picked at random. What is the probability that it is red?

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

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

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

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

   (1 mark)

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5. Question 5

   3 marks

   In 200 tosses of a coin, a head appeared 90 times. Find the experimental probability of getting a tail.

   (3 marks)

   Marking scheme

   Experimental probability uses what actually happened: $\frac{\text{times the event occurred}}{\text{total trials}}$. (1)

   A toss is either a head or a tail, so the tails are $200-90=110$. (1)

   $P(\text{tail})=\frac{110}{200}=\frac{11}{20}$. (1)

   Final answer: $\frac{11}{20}$, or $0.55$.

6. Question 6

   1 mark

   A fair die is rolled once. What is the probability of getting a number greater than 4?

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

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

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

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

   (1 mark)

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7. Question 7

   1 mark

   A fair die is rolled once. What is the probability of getting an even number?

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

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

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

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

   (1 mark)

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8. Question 8

   1 mark

   A fair die is rolled once. What is the probability of getting a 4?

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

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

   C. 6

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

   (1 mark)

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9. Question 9

   3 marks

   A bag contains 4 red, 6 green and 2 blue sweets. One sweet is picked at random.

   (a) Find the probability that it is green. (1 mark)

   (b) Find the probability that it is not red. (2 marks)

   Marking scheme

   The bag holds $4+6+2=12$ sweets, and probability is $\frac{\text{favourable}}{\text{total}}$. (1)

   (a) Six of the twelve are green: $P(\text{green})=\frac{6}{12}=\frac{1}{2}$. (1)

   (b) "Not red" means the $6$ green and $2$ blue, that is $8$ sweets: $P=\frac{8}{12}=\frac{2}{3}$. (1)

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

10. Question 10

    1 mark

    A bag contains 6 white and 4 black balls. A ball is picked at random. What is the probability that it is black?

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

    B. $\frac{4}{6}$

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

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

    (1 mark)

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11. Question 11

    1 mark

    What is the probability of a certain (sure) event?

    A. 0

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

    C. 1

    D. 100

    (1 mark)

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12. Question 12

    1 mark

    A bag has 4 red, 3 green and 5 yellow beads. A bead is picked at random. What is the probability that it is green?

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

    B. $\frac{3}{4}$

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

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

    (1 mark)

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13. Question 13

    1 mark

    A fair die is rolled once. What is the probability of getting an odd number?

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

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

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

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

    (1 mark)

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