A common way for two people to settle a frivolous dispute is to play a game of r

Question

A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each perso Scissors 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 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 50% of the time, and roommate B chooses rock 63% of the time; roommate A selects paper 4596 of the time, and roommate B selects paper 36% of the time; roommate A chooses scissors 5% of the time, and roommate B chooses scissors 1% 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? P(A) = 0.38 P(A)0.67 P(A) = 0.31 P(A) = 0.22

Explanation / Answer

probabilities are assigned using the empirical (experimental) probability

P(A) =P(A rock and B scissor+A scissor and B paper +A paper & B rock)=0.5*0.01+0.05*0.36+0.45*0.63=0.31

P(C)=P( both rock+both paper+both scissors)=0.5*0.63+0.45*0.36+0.05*0.01=0.48

P(B)=1-P(A)-P(C) =1-0.31-0.48=~0.22

Ac =event B or event C

the probability of Ac is 0.6935 ~0.69

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.