Probability — O/L Mathematics

How do I practise Probability?

3 questions with worked solutions

1. A fair six-sided die is rolled once. Find the probability of obtaining a number that is a multiple of 3.
   Show worked solution

   The sample space is S = {1,2,3,4,5,6}, so n(S) = 6. The multiples of 3 are 3 and 6, so the favourable outcomes are {3,6}, giving n(A) = 2. Therefore, P(multiple of 3) = n(A)/n(S) = 2/6 = 1/3.
   Modelled on: the O/L Mathematics examination pattern
2. A bag contains 4 red balls, 5 blue balls and 6 green balls. One ball is drawn at random. Find the probability that it is either red or blue.
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   Total number of balls = 4 + 5 + 6 = 15. The events 'red' and 'blue' are mutually exclusive because a ball cannot be both red and blue. P(red) = 4/15, P(blue) = 5/15. Therefore, P(red or blue) = 4/15 + 5/15 = 9/15 = 3/5.
   Modelled on: the O/L Mathematics examination pattern
3. Two fair dice are rolled. Find the probability that the sum of the numbers obtained is 8.
   Show worked solution

   There are 6 × 6 = 36 equally likely outcomes. The outcomes with sum 8 are (2,6), (3,5), (4,4), (5,3), (6,2) — a total of 5 outcomes. Therefore, P(sum = 8) = 5/36.
   Modelled on: the O/L Mathematics examination pattern

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Where does Probability fit in the syllabus?

Grade 10 · Term 3 · Grade 11 · Term 3