In a game, 2 players each flip a coin. I fboth land on heads, player A gets 2 points and player Bioses 1 points. Ifboth land on tails, player B gets 2 points and player A loses 1 point. Find the expected value of the game for each player.

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joaobezerra joaobezerra · Answer 1 · 2021-12-15T11:50:52+01:00

Building a probability distribution, it is found that the expected value for both players is of 0.25 points.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the four possible outcomes, considering Player A - Player B, are:

H - H

T - H

H - T

T - T

That is, considering a success as the number of heads, the distribution is:

[tex]P(X = 0) = 0.25[/tex]

[tex]P(X = 1) = 0.5[/tex]

[tex]P(X = 2) = 0.25[/tex]

For Player A, the earnings of each outcome are: -1, 0 and 2

Hence, the expected value is:

[tex]E_A(x) = -1(0.25) + 0(0.5) + 2(0.25) = 0.25[/tex]

For Player B, the earning of each outcome are: 2, 0 and -1.

Hence:

[tex]E_B(x) = 2(0.25) + 0(0.5) - 1(0.25) = 0.25[/tex]

The expected value for both players is of 0.25 points.

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