your methods as well as on the accuracy and completeness of your 1. The table summarizes the relationship between two categorical variables, grade level and the student's answer to the question, "Do you eat regularly in the school cafeteria?" Grade 9th 130 18 148 Eat in café? 11th 122 88 210 10th 12th Yes 175 68 No 34 170 Total 209 238 a. If you choose a student at random, what is the probability they eat regularly in the cafeteria? Total 495 310 805 b. If you choose a student at random, what is the probability they eat regularly in the cafeteria, given that they are in 10th grade? c. If you choose a student at random, are the events "10th grade" and "eats regularly in the cafeteria" independent? Explain how you know.

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AP Statistics
Unit 4 Free Response
Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of
your methods as well as on the accuracy and completeness of your results and explanations.
Name
1. The table summarizes the relationship between two categorical variables, grade level and the
student's answer to the question, "Do you eat regularly in the school cafeteria?"
Grade
Eat in
café?
9th
130
18
148
Yes
No
Total
11th
122
88
210
Pd
10th
12th
175
68
34
170
209
238
a. If you choose a student at random, what is the probability they eat regularly in the cafeteria?
Total
495
310
805
b. If you choose a student at random, what is the probability they eat regularly in the cafeteria, given
that they are in 10th grade?
c. If you choose a student at random, are the events "10th grade" and "eats regularly in the cafeteria"
independent? Explain how you know.
b. Find the probability that the team wins the debate.
2. On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35%
are Juniors, and 45% are Seniors. A team member is selected randomly to give the closing argument
for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning
the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes,
the probability of winning is 0.85.
a. Sketch a tree diagram to model this process.
Transcribed Image Text:AP Statistics Unit 4 Free Response Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Name 1. The table summarizes the relationship between two categorical variables, grade level and the student's answer to the question, "Do you eat regularly in the school cafeteria?" Grade Eat in café? 9th 130 18 148 Yes No Total 11th 122 88 210 Pd 10th 12th 175 68 34 170 209 238 a. If you choose a student at random, what is the probability they eat regularly in the cafeteria? Total 495 310 805 b. If you choose a student at random, what is the probability they eat regularly in the cafeteria, given that they are in 10th grade? c. If you choose a student at random, are the events "10th grade" and "eats regularly in the cafeteria" independent? Explain how you know. b. Find the probability that the team wins the debate. 2. On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors, and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. a. Sketch a tree diagram to model this process.
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