Question

The table below shows the relationship between age group and type of bet owned.

Part A: Complete the table by filling in the missing values
Age Group Dog Cat Other Total

Under 20 25 18 55

20-50 22 18 60

51+ 15 11 50


Total 60 64 165



Part B: Are the events "Under 20" and "Dog Owner" independent? Explain.

Answer 1

Part A — completed table

Age Group | Dog | Cat | Other | Total
- Under 20 | 25 | 18 | 12 | 55
- 20–50 | 20 | 22 | 18 | 60
- 51+ | 15 | 24 | 11 | 50
Total | 60 | 64 | 41 | 165

(Computed: Under 20 Other = 55−25−18 = 12; 20–50 Dog = 60−22−18 = 20; 51+ Cat = 50−15−11 = 24; Other total = 12+18+11 = 41.)

Part B — independence check

P(Under 20) = 55/165 = 1/3 ≈ 0.3333
P(Dog) = 60/165 = 4/11 ≈ 0.3636
P(Under 20 and Dog) = 25/165 = 5/33 ≈ 0.1515

If independent, P(Under 20 and Dog) would equal P(Under 20)·P(Dog) = (1/3)·(4/11) = 4/33 ≈ 0.1212, but 5/33 ≠ 4/33. Equivalently, P(Dog | Under 20) = 25/55 = 5/11 ≈ 0.4545 ≠ P(Dog).

Therefore the events "Under 20" and "Dog owner" are not independent.