A local arcade is hosting a tournament in which contestants play an arcade game with possible scores ranging from 0 to 20. The arcade has set up multiple game tables so that all contestants can play...


A local arcade is hosting a tournament in which contestants play an arcade game with possible scores ranging from 0 to 20. The arcade has set up multiple game tables so that all contestants can play the game at the same time; thus contestant scores are independent. Each contestant’s score will be recorded as he or she finishes, and the contestant with the highest score is the winner.
After practicing the game many times, Josephine, one of the contestants, has established the probability distribution of her scores, shown in the table below.


Crystal, another contestant, has also practiced many times. The probability distribution for her scores is shown in the table below.


Calculate the expected score for each player.


Suppose that Josephine scores 16 and Crystal scores 17. The difference (Josephine minus Crystal) of their scores is –1. List all combinations of possible scores for Josephine and Crystal that will produce a difference (Josephine minus Crystal) of –1, and calculate the probability for each combination.


Find the probability that the difference (Josephine minus Crystal) in their scores is –1.


Josephine's Distribution<br>Score<br>16<br>17<br>18<br>19<br>Probability<br>0.10<br>0.30<br>0.40<br>0.20<br>

Extracted text: Josephine's Distribution Score 16 17 18 19 Probability 0.10 0.30 0.40 0.20
Crystal's Distribution<br>Score<br>17<br>18<br>19<br>Probability<br>0.45<br>0.40<br>0.15<br>

Extracted text: Crystal's Distribution Score 17 18 19 Probability 0.45 0.40 0.15

Jun 01, 2022
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