There is a loss of to the player in carnival game.
Further explanation:
In the question it is given that in a carnival game it costs to play each time.
The amount of money received after winning a game is .
The probability of winning a game is .
Consider the probabilityof winning a game as .
The probablity of lossing a game is calculated as follows:
Consider the amount of money received by winning a game as .
Expected return to player is calculated as follows:
......(1)
If a person won a game then he must received and the amount of money paid for playing one game is .
This implies that in winning a game there is a gain of and if a player lost a game then there is a loss of .
Figure 1 (attached in the end) represents the different cases of winning and loosing.
Using the equation (1), the expected value of the amount to be received by a player is calculated as follows:
The value of as obtained above is which is a negative value.
The negative value implies that there is a loss to the player of .
Thus, there is a loss of to the player in carnival game.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Probability
Keywords: Probabilty, expected value, loss, profit, carnival game, 7 dollars, win $100, 1/50, winning, expected return, mathematics, sample space, money gain, money paid.