Prize Winner, Part 2
Resources for this lesson:
Key Terms:
Independent event
Dependent event
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> Teacher Resources: Instructional Notes
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 
0 
1 
2 
3 
4 
5+ 
Total 
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 
6326 
1079 
1019 
380 
103 
40 
8947 
Check Your Understanding
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 


Age of Head of Household 
0 
1 
2 
3 
4 
5+ 
Total 
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 
6326 
1079 
1019 
380 
103 
40 
8947 
In mathematics, it is never good to draw such a conclusion off of one example. Try another.
Check Your Understanding
Based on the last two exercises, is the number of children living in a household independent or dependent of the age of the head of the household?
Remember, the conditional probability is generally not equal to the probability P(B). This is because the Event A gives us information about whether or not Event B occurs. For this last example, knowing the age of the head of the household (Event A) gives us information about whether or not there are likely to be children living in the household (Event B).