Question

In the game of roulette, a player can place a $10 bet on the number 6 and have a 1/38 probability of winning. If the me...

In the game of roulette, a player can place a $10 bet on the number 6 and have a 1/38 probability of winning. If the metal ball lands on 6, the player gets to keep the $10 paid to play the game and the player is awarded an additional $350. Otherwise, the player is awarded nothing and the casino takes the player's $10. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?

The expected value is $___

The player would expect to lose about $__

In the game of roulette, a player can place a $10

0 0
Add a comment Improve this question Transcribed image text
Answer #1
Concepts and reason

Discrete variable: A variable is said to be discrete variable, if it is countable.

The table form of the discrete probability distribution is,

X X X , ......
Px(x) P(x) P(x) ...... P(x,)

The mean of a random variable represents what we would expect to happen in long run, it is also called the expected value, E(X)

Fundamentals

Formula for expected values and variance for discrete probability distribution are:

E(X)= x,P(x)+ x,P(x2)+....+x,P(x,)= XxP(x)

For the discrete variable, all the outcomes are either whole numbers or integers.

The winning amount of the player is $350.

The probability of winning the game is

Implies, the probability of losing the games is

The player gets to keep the $10 paid to pay the game.

Compute the expected value of the game to the player

E(X)-ΣπP(x)
= XP(x)+x,P(x,)
= 350% (-10) (18)
=-0.52632
38
8-0.5263

He expects to lose an average of about 52.6 cents per game.

The player's expected value is losing $0.5263.

When the game is played 1000 times, the amount expected to lose is1000x(-$0.5263) = $526.3

On playing for 1000 rounds, the player expected to lose about $526.3.

Ans:

The expected value is -$0.5263.

Add a comment
Know the answer?
Add Answer to:
In the game of roulette, a player can place a $10 bet on the number 6 and have a 1/38 probability of winning. If the me...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • In the game of​ roulette, a player can place a $10 bet on the number 16...

    In the game of​ roulette, a player can place a $10 bet on the number 16 and have a 1/38 chance of probability chance of winning. If the metal balls lands on 16, the player gets to keep the $10 paid to play the game and the player is awarded an additional $350. Otherwise, the player is awarded nothing and the casino takes the takes the player's $10. What is the expected value of the game to the player? If...

  • In the game of​ roulette, a player can place a ​$99 bet on the number 11...

    In the game of​ roulette, a player can place a ​$99 bet on the number 11 and have a (1/38) probability of winning. If the metal ball lands on 11 the player gets to keep the $9 paid to play the game and the player is awarded an additional $315. Otherwise, the player is awarded nothing and the casino takes the​ player's $9. What is the expected value of the game to the​ player? If you played the game 1000​...

  • In the game of​ roulette, a player can place a ​$9 bet on the number 28...

    In the game of​ roulette, a player can place a ​$9 bet on the number 28 and have a StartFraction 1 Over 38 EndFraction probability of winning. If the metal ball lands on 28​, the player gets to keep the ​$9 paid to play the game and the player is awarded an additional ​$315. ​ Otherwise, the player is awarded nothing and the casino takes the​ player's ​$9. What is the expected value of the game to the​ player? If...

  • In the game of roulette, a player can place a 55 bet on the number 9...

    In the game of roulette, a player can place a 55 bet on the number 9 and have a probability of winning. If the metal ball lands on 9, the player gets to keep the $5 paid to play the game and the player is awarded an additional $175. Otherwise, the player is awarded nothing and the casino takes the player's $5. What is the expected value of the game to the player? If you played the game 1000 times,...

  • In the game of roulette, a player can place a $5 bet on the number 6...

    In the game of roulette, a player can place a $5 bet on the number 6 and have a 1/38 probability of winning. If the metal ball lands on 6 , the player gets to keep the $5 paid to play the game and the player is awarded an additional $175 . Otherwise, the player is awarded nothing and the casino takes the player's $5 . What is the expected value of the game to the player? The expected value...

  • In the game of​ roulette, a player can place a ​$8 bet on the number 9...

    In the game of​ roulette, a player can place a ​$8 bet on the number 9 and have a 1/ 38 probability of winning. If the metal ball lands on 9​, the player gets to keep the ​$8 paid to play the game and the player is awarded an additional ​$280. ​Otherwise, the player is awarded nothing and the casino takes the​ player's ​$8. Find the expected value​ E(x) to the player for one play of the game. If x...

  • In the game of​ roulette, a player can place a ​$10bet on the number 25and have...

    In the game of​ roulette, a player can place a ​$10bet on the number 25and have a 1/38probability of winning. If the metal ball lands on 25​, the player gets to keep the $10 paid to play the game and the player is awarded an additional ​$350.Otherwise, the player is awarded nothing and the casino takes the​ player's ​$10. Find the expected value​ E(x) to the player for one play of the game. If x is the gain to a...

  • 7. In the game of American roulette, a player can place a d probability of winning. If the metal ...

    7. In the game of American roulette, a player can place a d probability of winning. If the metal ball lands aS 5 bet on the manber 17 and h on 17, the player gets to keep the to play the game and the player is aware is awarded mothing, and the casino takes the player's s is "warded anadditional S 175-Oherwise, the player a probability distribution for the proft of the same to the plnyer JAptl b) What is...

  • Roulette: In the game of ro winning. If the metal ball lan player's $5. What is...

    Roulette: In the game of ro winning. If the metal ball lan player's $5. What is the expce much would you expect to lose? n the game of roulette, a player can place a $5 bet on the number 17 and have a 1/38 probability of the metal ball lands on 17, the player wins S180 (gain of $ 175) Otherwise, the casino takes the What is the expected value of the game to the player? If you played the...

  • I am wondering if you can help me out with these questions. I am very confused....

    I am wondering if you can help me out with these questions. I am very confused. 1. A math teacher gave her class two tests. While 70% of the class passed the first test and 75% of the class passed the second test, only 65% of the class passed both. Given that the students failed the first test, what probability of those will passed the second test? 2. In the game of roulette, a player can place a $5 bet...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT