Ratio, Probability and Statistics KS3 Maths Worksheets, Questions and Revision

A bag contains 15 counters: 6 yellow, 5 purple and 4 orange. A counter is picked at random, its colour is noted, then it is put back before a second counter is picked at random. (a) Find the probability that the first counter is purple. (b) Find the probability that both counters picked are orange.

1. There are 15 counters in total, so P(first counter purple) = 5/15.
2. Simplify 5/15 by dividing the numerator and denominator by 5 to get 1/3.
3. Since the counter is replaced before the second pick, the two picks are independent, so multiply their individual probabilities.
4. P(orange) on a single pick = 4/15.
5. P(both counters orange) = 4/15 x 4/15 = 16/225.