Alexa1 and Zoltan2 play the following game: AZ-game: Step 1: Alexa chooses a uniformly random element from the set 1,2,3). Let a denote the element that Alexa chooses. Step 2: Zoltan chooses a uniformly random element from the set 1,2,3). Let 2 denote the element that Zoltan chooses. Step 3: Using one of the three strategies mentioned below, Alexa chooses an element from the set {1.23 X { Let a, denote the element that Alexa chooses Step 4: Using one of the three strategies mentioned below, Zoltan chooses an element from the set {1,2,3) \ 1z). Let z' denote the element that Alexa chooses The AZ-game is a success if

MinMin Strategy: In Step 3, Alexa chooses the smallest element in the set 1, 2, 3\a], and oltan chooses the smallest element in the set {1.23}

Describe the sample space for this strategy.

For this strategy, determine the probability that the AZ-game is a success.

MinMax Strategy: In Step 3, Alexa chooses the smallest element in the set {1,2,3)\1a), and Zoltan chooses the largest element in the set 1,2,3

Describe the sample space for this strategy.

For this strategy, determine the probability that the AZ-game is a success.

Random Strategy: In Step 3, Alexa chooses a uniformly random element in the set { 1, 2. 3X {, and oltan chooses a uniformly random element in the set { 1.23

Describe the sample space for this strategy.

For this strategy, determine the probability that the AZ-game is a success.