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 choos

Question

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.

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Thu Giang 3 years 2021-07-19T07:23:26+00:00 1 Answers 43 views 0

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  1. RuslanHeatt
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    2021-07-19T07:25:04+00:00
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    Answer:

    0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.

    Step-by-step explanation:

    Independent events:

    If two events are independent, the probability of both happening is the multiplication of their probabilities.

    Rock-paper-scissors rules:

    A player that choose rocks beats one who chooses scissors.

    A player that choose paper beats one who chooses rocks.

    A player that choose scissors beats one who chooses paper.

    Probability that roommate A wins the game and thus does not have to wash the dishes.

    3 possible events:

    Roommate A – Rocks(21% of the time) and Roommate B – Scissors(18% of the time)

    So

    p_R = 0.21*0.18 = 0.0378

    Roommate A – Paper(39% of the time) and Roommate B – Rocks(61% of the time).

    So

    p_P = 0.39*0.61 = 0.2379

    Roommate A – Scissors(40% of the time) and Roommate B – Paper(21% of the time).

    So

    p_S = 0.4*0.21 = 0.084

    Probability of roommate A winning:

    p = p_R + p_P + p_S = 0.0378 + 0.2379 + 0.084 = 0.3597

    0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.

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