SOLUTION: 9 In a two person game, four coins are tossed. If exactly two come up heads, you win. If anything else comes up, you lose. Does each player have an equal chance of winning the game

Question 178826: 9 In a two person game, four coins are tossed. If exactly two come up heads, you win. If anything else comes up, you lose. Does each player have an equal chance of winning the game ? Explain why or why not
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let's make a table of each coin toss and whether its a heads or tail (H or T).
Then in the last column, sum the number of heads in all four tosses.
4 coins with 2 sides gives 16 possible outcomes.
H H H H 4
H H H T 3
H H T H 3
H H T T 2
H T H H 3
H T H T 2
H T T H 2
H T T T 1
T H H H 3
T H H T 2
T H T H 2
T H T T 1
T T H H 2
T T H T 1
T T T H 1
T T T T 0
Of the 16, only 6 have exactly 2 heads.
That means you would win 6/16 times, and lose 10/16 times.
No, the game is not fair to you.
The other player has the advantage.
If it was fair, both would have 8/16 or 1/2 of the possible outcomes.
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