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](https://tex.z-dn.net/?f=p_R%20%3D%200.21%2A0.18%20%3D%200.0378)
Roommate A - Paper(39% of the time) and Roommate B - Rocks(61% of the time).
So
![p_P = 0.39*0.61 = 0.2379](https://tex.z-dn.net/?f=p_P%20%3D%200.39%2A0.61%20%3D%200.2379)
Roommate A - Scissors(40% of the time) and Roommate B - Paper(21% of the time).
So
![p_S = 0.4*0.21 = 0.084](https://tex.z-dn.net/?f=p_S%20%3D%200.4%2A0.21%20%3D%200.084)
Probability of roommate A winning:
![p = p_R + p_P + p_S = 0.0378 + 0.2379 + 0.084 = 0.3597](https://tex.z-dn.net/?f=p%20%3D%20p_R%20%2B%20p_P%20%2B%20p_S%20%3D%200.0378%20%2B%200.2379%20%2B%200.084%20%3D%200.3597)
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.