O Aplia: Student Question × t MindTap-Cengage Lear. × Frequency Distribution TX
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O Aplia: Student Question × t MindTap-Cengage Lear. × Frequency Distribution TX -StudyBlue X | Facebook GI Academics-Academic p . i c Q Search courses.aplia.com/af/servlet/quiz?quiz_action-t bGuide QNAPC0A80 10 1 0000003b8d74e0090000&ctx;=delil.martinez 6. Rock-paper-scissors #3 Aa Aa A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person simultaneously displays a hand signal to indicate a rock, a piece of paper, or a pair of scissors. Rock beats scissors, scissors beats paper, and paper beats rock. If both players select the same hand signal, the game results in a tie. Scissors beats paper Paper beats rock Two roommates, roommate A and roommate B, are expecting company and are arguing over who should have to wash the dishes before the company arrives. Roommate A suggests a game of rock-paper-scissors to settle the dispute. Rock beats scissors Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 21% of the time, and roommate B chooses rock 61% of the time; roommate A selects paper 39% of the time, and roommate B selects paper 21% of the time; roommate A chooses scissors 40% of the time, and roommate B chooses scissors 18% of the time. (These choices are made randomly and independently of each other.) The probabilities were assigned using the Define event A as the event that roommate A wins the game and thus does not have to wash the dishes. What is P(A), the probability of event A? RA) = 0.67 RA) = 0.22 P(A) = 0.36 P(A)-0.76 59:30 6:39 PM 9/14/2017Explanation / Answer
Probability of A choosing Rock = PA(R) = 0.36
Probability of A choosing Paper = PA(P) = 0.32
Probability of A choosing Scissor = PA(S) = 0.32
Probability of B choosing Rock = PB(R) = 0.22
Probability of B choosing Paper = PB(P) = 0.25
Probability of B choosing Scissor = PB(S) = 0.53
What is P(A), the probability of event A?
Note: Choices of A are independent to that of B.
There are following possibilites of A winning,
PA = P1 + P2 + P3 = 0.1908+0.08+0.0704 =0.3412
Answer: Option C
What is P(C), the probability of event C?
There are following possibilites of a Tie,
PC = P1 + P2 + P3 = 0.0792+0.1696+0.08 = 0.3288 = 0.33 (Approx.)
Answer: Option B
What is P(B), the probability of event B?
There are following possibilites of B winning,
PB = P1 + P2 + P3 = 0.0704+0.1696+0.09 = 0.33
Answer: Option C
What is the complement of event A?
The complement of A winning is either A losing (Event B) or a Tie (Event C).
Hence Ac = Event B or Event C
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