GB-18-03-001 · Venn diagram regions
In a group of 55 students, 41 play chess, 27 play tennis and 19 do both.
(a) Work out how many students do neither activity.
(b) Find the probability that a randomly chosen student plays chess but not tennis.
Part (a)
Venn Diagrams
Booklet p. 62
Method
1) Fill the intersection first
2) Subtract it from each set total to get the exclusive regions
3) Subtract the union from the overall total for neither
4) Use the required region for the probability
Worked Example (GB-18-03-001 · Part (a))
Work out how many students do neither activity.
1)
Start with 19 in the intersection. Chess only = 41 − 19 = 22; tennis only = 27 − 19 = 8.
2)
3)
Neither = .
Ans =
6
Part (b)
Venn Diagrams
Booklet p. 62
Method
1) Fill the intersection first
2) Subtract it from each set total to get the exclusive regions
3) Subtract the union from the overall total for neither
4) Use the required region for the probability
Worked Example (GB-18-03-001 · Part (b))
Find the probability that a randomly chosen student plays chess but not tennis.
1)
Start with 19 in the intersection. Chess only = 41 − 19 = 22; tennis only = 27 − 19 = 8.
2)
3)
Ans =