Prize Winner, Part 2

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A community fair is happening in the town of Alexandria. The community board of directors has asked Khalid, Justyce, Andrew, Marissa and Allyson to create games for the children who come to the fair.

So far, Khalid, Justyce, Andrew, Marissa and Allyson have created a duck pond game and a balloon popping game.

The next game they design is a corn hole game, as shown below.

This is a corn hole game platform

The object of this game is to stand in front of the board and toss bean bags into the hole. The winner is the person who scores the most points by tossing the bags into the holes. In some games, points are also awarded for “hanging” bags (bags that are hanging onto the edge of the hole) and bags that land on the board.

Khalid, Justyce, Andrew, Marissa and Allyson are designing the corn hole game for the community fair. Each person participating in the game will toss four bean bags, attempting to land bean bags into the hole. A small candy prize is awarded for each bag a person can land completely into the hole. A person can win up to four candies.

To make the game challenging to older participants, Khalid suggests they adjust where people stand according to age. Children will stand directly in front of the board, at 0 feet. Teenagers will stand 13.5 feet in front of the board. Adults will stand 27 feet in front of the board.

To check the fairness of their game, they decide to do a trial run and record people’s scores in a two-way table like the one shown below.

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
Teens (13≤age<20) Distance from Board 13.5 feet
Adults Age≥20 Distance from Board 27 feet
Total People

They set up the game at the local mall and invite 300 people to try it out. For this game, a person wins a candy prize equal to the total number of bags they land completely in the hole. For example, a person who lands 3 bags into the hole will win 3 candies.

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
Adults Age≥20 Distance from Board 27 feet	3	8	25	16	12	64
Total People	5	45	109	76	65	300

Check Your Understanding

 

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