Venn Diagrams Thirty pupils from Mr Evans class

Venn Diagrams Thirty pupils from Mr Evans’ class are competing in the Aberglas School sports day. Of these: • 22 are running in a race; • 15 are taking part in a jumping competition; • 2 are not running or jumping. Ɛ Running Jumping How many pupils are running but not jumping?

Thirty pupils from Mr Evans’ class are competing in the Aberglas School sports day. Of these: • 22 are running in a race; • 15 are taking part in a jumping competition; • 2 are not running or jumping. 2 pupils not running or jumping 28 – 22 = 6 pupils jumping but not running 2 Ɛ 13 30 – 2 = 28 pupils running or jumping or both 9 6 Running 28 – (13 + 6) = 9 pupils jumping and running How many pupils are running but not jumping? Jumping 28 – 15 = 13 pupils running but not jumping

Now let us also consider the pupils who are taking part in the throwing competition. Each of the 30 pupils are taking part in at least one competition. As before: • 22 are running in a race; • 15 are taking part in a jumping competition; • 2 are not running or jumping. Also: Running • 5 are taking part in all competitions; • 3 are running and throwing but not jumping; • 1 is jumping only. Jumping Ɛ Throwing Complete the Venn diagram.

• 5 are taking part in all competitions; • 3 are running and throwing but not As before: • 22 are running in a race; • 15 are taking part in a jumping competition; • 2 are not running or jumping. Also: Every pupil is taking part Running Jumping Ɛ 10 2 not running or jumping 4 1 5 5 taking part in everything 3 running and throwing but not jumping; • 1 is jumping only. 5 3 0 2 Throwing 15 – (5 + 1) = 4 running and jumping but not throwing 1 jumping only 28 – 15 = 13 running but not jumping 13 – 3 = 10 running only 28 – 22 = 6 jumping but not running 6 – 1 = 5 jumping and throwing but not running

Given that Harry is taking part in a jumping competition, what is the probability that he will also be throwing? Running Jumping Ɛ 4 10 1 5 5 3 2 0 Throwing Probability = 10 or 2 15 3