Probability: practice questions

6 questions · 11 marks · free, no account · Read the notes first

1. Question 1Multiple choice · 1 mark

   Two fair dice are thrown. Find the probability that the sum of the numbers is 7.

   A

   $\dfrac{7}{36}$

   B

   $\dfrac{1}{6}$

   C

   $\dfrac{5}{36}$

   D

   $\dfrac{1}{12}$

2. Question 2Multiple choice · 1 mark

   A bag has 4 red balls and 6 blue balls. Two balls are drawn at random without replacement. Find the probability that both are red.

   A

   $\dfrac{4}{25}$

   B

   $\dfrac{2}{5}$

   C

   $\dfrac{2}{15}$

   D

   $\dfrac{1}{15}$

3. Question 3Multiple choice · 1 mark

   $A$ and $B$ are independent events with $P(A) = 0.3$ and $P(B) = 0.5$. Find the probability that at least one of them happens.

   A

   $0.8$

   B

   $0.15$

   C

   $0.35$

   D

   $0.65$

4. Question 4Multiple choice · 1 mark

   A game costs $10 to play. A fair die is thrown once; a player who gets a 6 receives $30, otherwise nothing. Find the expected gain of a player.

   A

   −$5

   B

   $5

   C

   $0

   D

   −$10

5. Question 53 marks

   3 students are chosen at random from 5 boys and 4 girls. Find the probability that exactly 2 girls are chosen.

   Show worked solution

   $$P = \frac{C^4_2 \times C^5_1}{C^9_3} \qquad \text{1M + 1M}$$ $$= \frac{5}{14} \qquad \text{1A}$$
6. Question 64 marks

   The probabilities that Ken passes Chinese and English are 0.8 and 0.7 respectively, and the results are independent. Find the probability that Ken passes

   (a) both subjects;

   (b) exactly one of the subjects.

   Show worked solution

   (a) $P(\text{both}) = 0.8 \times 0.7 = 0.56$ 1A

   (b) $P(\text{exactly one}) = 0.8 \times 0.3 + 0.2 \times 0.7$ 1M + 1M

   $= 0.38$ 1A