4.5 Probability basicsIB Maths: Applications and Interpretation SL: Subtopic test

1. 1
   A bag contains 5 red, 3 blue and 2 green counters. One counter is chosen at random.

   (a)

   Find the probability that the counter is blue.

   [1 mark]

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

   (b)

   Find the probability that the counter is not green.

   [1 mark]

   • A$\frac{1}{5}$
   • B$\frac{1}{2}$
   • C$\frac{4}{5}$
   • D$\frac{3}{10}$

   (c)

   The counter is returned to the bag and the experiment is repeated 150 times. Find the expected number of times that a red counter is chosen.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A fair six-sided die is rolled once and a fair coin is tossed once.

   (a)

   How many outcomes are there in the sample space for rolling the die and tossing the coin?

   [1 mark]

   • A$8$
   • B$12$
   • C$6$
   • D$24$

   (b)

   Find the probability of obtaining an even number and a head.

   [1 mark]

   • A$\frac12$
   • B$\frac{1}{12}$
   • C$\frac{1}{6}$
   • D$\frac14$

   (c)

   Find the probability of obtaining a number less than 3 and a tail.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A spinner has four equal-sized sectors numbered 1 to 4. It is spun 200 times and the results are: sector 1 occurs 38 times, sector 2 occurs 62 times, sector 3 occurs 55 times and sector 4 occurs 45 times.

   (a)

   (i) Find the relative frequency of sector 2.
   (ii) Assuming that the spinner is fair, write down the theoretical probability of sector 2.

   [3 marks]

   (b)

   The spinner is now spun a further 600 times.
   (i) Using the relative frequency from the first 200 spins, estimate the number of times that sector 2 will occur.
   (ii) Find the number of times that sector 2 is expected to occur if the spinner is fair.
   (iii) Comment on whether the results so far suggest that the spinner is biased.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school has 320 students: 128 are in DP1, 112 are in DP2 and the rest are in lower years. A student is chosen at random. School records show that the probability that a given student is absent on any day is 0.075.

   (a)

   (i) Find the probability that the student is in the lower years.
   (ii) Find the probability that the student is not in DP1.
   (iii) Find the expected number of students absent on a given day.

   [6 marks]

   (b)

   On 10 Monday mornings the school made 3200 student registrations in total, of which 288 were absences.
   (i) Find the relative frequency of absence on these Mondays.
   (ii) Use this relative frequency to estimate the expected number of absent students on a Monday.
   (iii) Find the number of absences expected over the 3200 registrations if the probability of absence is 0.075, and comment on your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions