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STatiana [176]
3 years ago
13

Suppose you want to play a carnival game that costs 7 dollars each time you play. If you win, you get $100. The probability of w

inning is 1⁄50. What is the expected value of the amount that you, the player, stand to gain?

Business
2 answers:
lilavasa [31]3 years ago
8 0

Answer:

The correct answer would be $5

Explanation:

The formula to use is "Expected return to player" which is

E(x) = x.p(x)

where x is the return to player if they win

and p(x) is the probability of winning.

So here,

x = $100 (return to player for winning)

p(x) = 1/50 (probability of winning)

Therefore expected return to player is

E(x) = x.p(x)

= $100 x 1/50

= $100/50

= $2

Cost: $7

Expected return to player is $2.

Therefore Loss (to player) is Cost minus Expected return

= $7 - $2 = $5 <---- expected value for the carnival to gain,

The loss to the player is the carnival's gain. It's $5.

ololo11 [35]3 years ago
6 0

There is a loss of \bf \$\ 5 to the player in carnival game.

Further explanation:

In the question it is given that in a carnival game it costs \$\ 7 to play each time.

The amount of money received after winning a game is \$\ 100.

The probability of winning a game is \frac{1}{50}.

Consider the probabilityof winning a game as P.

The probablity of lossing a game is calculated as follows:

\begin{aligned}P'&=1-P\\&=1-\dfrac{1}{50}\\&=1-0.02\\&=0.98\end{aligned}

Consider the amount of money received by winning a game as X.

Expected return to player is calculated as follows:

\boxed{\text{E}(X)=XP(X)}                          ......(1)

If a person won a game then he must received \$\ 100 and the amount of money paid for playing one game is  \$\ 7.

This implies that in winning a game there is a gain of \$\ 93 and if a player lost a game then there is a loss of \$\ 7.

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:

\begin{aligned}\text{E}(x)&=\left(93\cdot 0.02\right)+\left((-7)\cdot 0.98\right)\\&=1.86-6.86\\&=-5\end{aligned}

The value of \text{E}(x) as obtained above is -5 which is a negative value.

The negative value \text{E}(x) implies that there is a loss to the player of \$\ 5.

Thus, there is a loss of \bf \$\ 5 to the player in carnival game.

Learn more:

1. A problem to determine the equation of line brainly.com/question/1646698

2. A problem on ray brainly.com/question/1251787

3. A problem to determine intercepts of a line brainly.com/question/1332667  

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.

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