Probability basics and sample spacesIB MYP Maths Extended: Subtopic test

1. 1
   A bag at a school fair in Nairobi holds 5 red counters, 3 blue counters and 2 green counters. One counter is taken from the bag at random.

   (a)

   What is the probability that the counter is blue?

   [1 mark]

   • A$\frac{3}{7}$
   • B$\frac{1}{3}$
   • C$\frac{3}{5}$
   • D$\frac{3}{10}$

   (b)

   What is the probability that the counter is not red?

   [1 mark]

   • A$\frac{3}{10}$
   • B$\frac{1}{2}$
   • C$\frac{7}{10}$
   • D$\frac{1}{5}$

   (c)

   Find the probability that the counter is red or green. Give a reason why you can add probabilities.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two fair four-sided spinners, each numbered 1 to 4, are spun and the two scores are added together.

   (a)

   How many outcomes are there in the sample space?

   [1 mark]

   • A$16$
   • B$8$
   • C$4$
   • D$10$

   (b)

   What is the probability that the total is 5?

   [1 mark]

   • A$\frac{1}{16}$
   • B$\frac{1}{5}$
   • C$\frac{1}{4}$
   • D$\frac{5}{16}$

   (c)

   Find the probability that the total is at least 7.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A fair coin is flipped and a fair spinner with three equal sections numbered 1, 2 and 3 is spun.

   (a)

   List the sample space. Find the probability of getting heads and an odd number.

   [3 marks]

   (b)

   Event $A$ is 'heads and the spinner shows 1'. Event $B$ is 'tails'. Explain why $A$ and $B$ are mutually exclusive, find $P(A\text{ or }B)$, and find the probability that neither $A$ nor $B$ happens.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   At a school fair in Manila, a player rolls two fair six-sided dice and adds the scores. The organiser is choosing the winning rule. Rule X: the player wins with a total of 7 or 11. Rule Y: the player wins with a prime total.

   (a)

   Using Rule X:
   (i) State the number of outcomes in the sample space.
   (ii) Find the probability that the total is 7.
   (iii) Find the probability that a player wins.
   (iv) Find the probability that a player does not win.

   [6 marks]

   (b)

   The prize is worth more than the entry fee, and the stall must make money for the school. Justify which rule the organiser should choose.

   [6 marks]

   Total for question 4: 12 marks

End of questions