Prize Winner, Part 2

Resources for this lesson:

People at the Mall Who Try the Game

Age Group

Number of people who landed
0
out of 4 bags thrown  in the hole

Number of people who landed
1
out of 4 bags thrown  in the hole

Number of people who landed
2
out of 4 bags thrown  in the hole

Number of people who landed
3
out of 4 bags thrown  in the hole

Number of people who landed
4
out of 4 bags thrown  in the hole

Total
People

Children
(age<13)
Distance from Board
0 feet

0

16

48

36

32

132

Teens
(13≤age<20)
Distance from Board
13.5 feet

2

21

36

24

21

104

Age≥20
Distance from Board
27 feet

3

8

25

16

12

64

Total People

5

45

109

76

65

300

Consider the following:

What is the probability of a person landing 3 bags in the hole, given that they stood at 27 feet?

This probability can be written as . How is this probability different than the ones you just answered?

This probability is different because it limits us to one specific group. The phrase “given that they stood  27 feet from the board”  means that we only look at the 64 people who stood 27 feet away from the board. Out of this group of 64 people, how many sank 3 bags into the hole? According to the table, 16 people fit this description. Thus,

Check this with the definition of conditional probability, .

= $\frac{\frac{16}{300}}{\frac{64}{300}}$

= $\frac{16}{64}=\frac{1}{4}$

It checks out correctly!