Experimental probability and expected frequencyIB MYP Maths Extended: Subtopic test

1. 1
   A spinner at a school in Kuala Lumpur has four equal sections, one of which is red. It is spun 200 times and lands on red 46 times.

   (a)

   What is the relative frequency of the spinner landing on red?

   [1 mark]

   • A$0.46$
   • B$0.25$
   • C$0.23$
   • D$0.77$

   (b)

   Use the relative frequency of red to estimate how many times the spinner would land on red in 500 spins.

   [1 mark]

   • A$125$
   • B$46$
   • C$230$
   • D$115$

   (c)

   Work out the theoretical probability of red and comment on whether the spinner appears to be fair.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A factory in Penang tests 400 light bulbs from one production line. Of these, 12 are faulty.

   (a)

   What is the relative frequency of a faulty bulb?

   [1 mark]

   • A$0.3$
   • B$0.03$
   • C$0.12$
   • D$33$

   (b)

   Use the relative frequency to estimate the number of faulty bulbs in a batch of 5000.

   [1 mark]

   • A$150$
   • B$15$
   • C$1500$
   • D$12$

   (c)

   Suggest how the factory could get a more reliable estimate of the probability that a bulb is faulty, and explain why this works.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student in Santiago flips a drawing pin 150 times and it lands point up 63 times. Another student flips the same pin 1000 times and it lands point up 412 times.

   (a)

   Work out the relative frequency of 'point up' for each student and state, with a reason, which is more reliable.

   [3 marks]

   (b)

   Combine both sets of results to give the best estimate of the probability that the pin lands point up. Use it to estimate the number of times the pin lands point up in 800 flips.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A games company in Seoul tests a six-sided die before using it in a board game. In a first test of 600 rolls the numbers 1 to 6 appear 80, 95, 98, 102, 104 and 121 times. In a second test of 6000 rolls the number 6 appears 1190 times.

   (a)

   Using the first test only, work out the relative frequency of a 6 and the number of 6s expected if the die were fair. Comment on whether the first test shows that the die is biased.

   [6 marks]

   (b)

   Use the second test to evaluate whether the die is fair. State what the company should do.

   [6 marks]

   Total for question 4: 12 marks

End of questions