1. GCSE Mathematics Problem Solving Data Higher Tier

2. There are 12 boys in Miss Jones’ Mathematics class. 5 have brown eyes, 4 have green eyes and 3 have blue eyes. She randomly chooses three different boys to answer her questions. What is the probability that at least one of the boys chosen will have green eyes? Brown eyes – 5 12 What does the question ask us to find? P(at least one green eyed boy) = ? Green eyes – 4 12 Blue eyes – 3 12 What information is given in the question?

3. Consider the possible outcomes GBrBl orGBrBr orGBlBl orGBlBr or GGBl orGGBr orGBlG or... Is there a quicker or easier way? P(at least one green) = 1 – P(no green) P(no green) = ? Consider how many pupils do not have green eyes Brown eyes + Blue eyes = 5 + 3 12 12 = 8 12 P(at least one green) + P(no green) = 1

4. P(at least one green) = 1 – P(no green) P(no green) = What did the question ask us to find? = 1 - 14 55 8 12 7 11 6 10 xx = 2 x 7 x 3 3 11 5 = 42 165 = 14 55 = 41 55