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.

Answer 1

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

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.