suppose that you are offered the following \deal.\ you roll a six - sided die. if you roll a 6, you win $10…

suppose that you are offered the following \deal.\ you roll a six - sided die. if you roll a 6, you win $10. if you roll a 3, 4 or 5, you win $2. otherwise, you pay $5.\na. complete the pdf table. list the x values, where x is the profit, from smallest to largest. round to 4 decimal places where appropriate.\nprobability\ndistribution table\n|x|p(x)|\n|\n|\n|\n|\n|\n|\nb. find the expected profit. $ (round to the nearest cent)\nc. interpret the expected value.\nthis is the most likely amount of money you will win.\nif you play many games you will likely win on average very close to $1.00 per game.\nyou will win this much if you play a game.\nd. based on the expected value, should you play this game?\nno, this is a gambling game and it is always a bad idea to gamble.\nno, since the expected value is negative, you would be very likely to come home with less money if you played many games.\nyes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.\nyes, because you can win $10.00 which is greater than the $5.00 that you can lose.\nyes, since the expected value is positive, you would be very likely to come home with more money if you played many games.

suppose that you are offered the following \deal.\ you roll a six - sided die. if you roll a 6, you win $10. if you roll a 3, 4 or 5, you win $2. otherwise, you pay $5.\na. complete the pdf table. list the x values, where x is the profit, from smallest to largest. round to 4 decimal places where appropriate.\nprobability\ndistribution table\n|x|p(x)|\n|\n|\n|\n|\n|\n|\nb. find the expected profit. $ (round to the nearest cent)\nc. interpret the expected value.\nthis is the most likely amount of money you will win.\nif you play many games you will likely win on average very close to $1.00 per game.\nyou will win this much if you play a game.\nd. based on the expected value, should you play this game?\nno, this is a gambling game and it is always a bad idea to gamble.\nno, since the expected value is negative, you would be very likely to come home with less money if you played many games.\nyes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.\nyes, because you can win $10.00 which is greater than the $5.00 that you can lose.\nyes, since the expected value is positive, you would be very likely to come home with more money if you played many games.

Answer

Explanation:

Step1: Determine the profit values and their probabilities

  • If roll 1 or 2, pay $5, so $X=- 5$. Probability $P(X = - 5)=\frac{2}{6}=\frac{1}{3}\approx0.3333$.
  • If roll 3, 4 or 5, win $2, so $X = 2$. Probability $P(X = 2)=\frac{3}{6}=0.5$.
  • If roll 6, win $10, so $X = 10$. Probability $P(X = 10)=\frac{1}{6}\approx0.1667$.

Step2: Calculate the expected value

The formula for the expected value $E(X)=\sum_{i}X_{i}P(X_{i})$. $E(X)=(-5)\times\frac{1}{3}+2\times\frac{1}{2}+10\times\frac{1}{6}$ $=-\frac{5}{3}+1+\frac{5}{3}$ $=1$

Step3: Interpret the expected value

The expected - value represents the average amount of money won per game over a large number of games.

Step4: Decide whether to play

Since the expected value $E(X)=1>0$, over many games, on average, more money will be won.

Answer:

a.

X P(X)
- 5 0.3333
2 0.5
10 0.1667
b. $1.00
c. If you play many games you will likely win on average very close to $1.00 per game.
d. Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games.