Anna and Bill are roommates. Each of them can choose whether to clean the apartment ("Clean") orleave it dirty ("Dirty"). If nobody cleans the apartment, they each get a payoff of zero. If they both cleanthe apartment, they each get a payoff of 4. If only one of them cleans, the person who leaves itdirty gets to enjoy a clean apartment without having to put in any effort. That person will receive apayoff of 5, while the person who does the cleaning will receive a payoff of 2.

1. In the mixed strategy Nash Equilibrium, what is the probability that Anna cleans the apartment? (Write the probability as a number between 0 and 1, with two decimal points, e.g. 0.50.)

2. In the mixed strategy Nash Equilibrium, what is the probability that Bill cleans the apartment?

3. In the mixed strategy Nash Equilibrium, what is the probability that both Anna and Bill clean the apartment?

4. In the mixed strategy Nash Equilibrium, what is the probability that at least one of the two roommatescleans the apartment?

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