Tonight, please complete the "Juana and Carroll" AP problem. This deals with expected value and the stuff we learned prior--so no binomial or geometric probability on this one.
Period B (or anyone who was absent or lost the paper): You can find the questions below. Enjoy!
AP Free Response
Problem:
A nearby video store is holding a tournament where
contestants play a video game with scores ranging from 0 to 20. There are
multiple game stations set up so that all contestants play simultaneously;
thus, contestant scores are independent. Each score will be recorded as a
player finishes, and the player with the highest score is the winner.
After practicing many times, Juana, one of the contestants,
has created the probability distribution of her scores, shown below.
Juana’s Distribution
Score
|
16
|
17
|
18
|
19
|
Probability
|
0.10
|
0.30
|
0.40
|
0.20
|
Carroll, another player, has also practiced multiple times
and created the probability distribution shown below.
Carroll’s
Distribution
Score
|
17
|
18
|
19
|
Probability
|
0.45
|
0.40
|
0.15
|
1. Find the expected score for each
player. Write your answer in a complete sentence, in context.
2. Suppose Juana scores 16 and Carroll
scores 17. The difference (J – C) of their scores is -1. Find all combinations
of possible scores for Juana and Carroll that will produce a difference (J – C)
of -1, and calculate the probability of each combination.
3. Calculate the probability that the
difference (J – C) between their scores is -1.
4. The following table lists all possible
differences in scores between Juana and Carroll and the associated
probabilities.
Distribution (Juana minus Carroll)
Difference
|
-3
|
-2
|
-1
|
0
|
1
|
2
|
Probability
|
0.015
|
0.325
|
0.260
|
0.090
|
5. Complete
the table and calculate the probability that Carroll’s score will be greater
than Juana’s score.
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