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

Question

03-11-2022
Mathematics

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

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SantosO786963 SantosO786963 · Answer 1 · 2022-11-03T13:09:50+01:00

The expected value for player A is:

[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]

The expected value of player B is:

[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]