# Prize Winner, Part 2

### Resources for this lesson:

Key Terms:

Independent event
Dependent event

As Khalid, Justyce, Andrew, Marissa and Allyson set up the games, they wonder how many children they could expect to show for the carnival.

Khalid collects data for their community comparing the age of the head of household to the number of children in the household.

Analysis of Number of Children Living in the Household compared to the

Age of the Head of the Household

Number of Children in the Household Age of Head of Household Total 18 – 24 25 – 44 45 – 64 65+ (years) Number of Households 0 1 2 3 4 5+ 135 59 34 7 3 2 240 667 435 627 279 70 30 2108 3091 544 333 91 28 7 4094 2433 41 25 3 2 1 2505 6326 1079 1019 380 103 40 8947

Is the number of children living in a household in this community independent or dependent of the age of the head of the household? If the answer to this question is that the events are independent, then.

Let’s check the above exercise, . would be . According to the table, the probability of having three children in a household is $\frac{380}{8947}$. This is not equal to the value we found for . Thus, the number of children in a household is dependent on the age of the head of the household.

Number of Children in the Household

(years)

0

1

2

3

4

5+

Total
Number of Households

18 – 24

135

59

34

7

3

2

240

25 – 44

667

435

627

279

70

30

2108

45 – 64

3091

544

333

91

28

7

4094

65+

2433

41

25

3

2

1

2505

Total
Number of Households

6326

1079

1019

380

103

40

8947

In mathematics, it is never good to draw such a conclusion off of one example. Try another.