Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $8. If you roll a 2, 3, 4 or 5, you win $3. Otherwise, you pay $8. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution TableXP(X)      b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value.If you play many games, on average, you will likely win, or lose if negative, close to this amount.You will win this much if you play a game.This is the most likely amount of money you will win.

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Asked Nov 7, 2019
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Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $8. If you roll a 2, 3, 4 or 5, you win $3. Otherwise, you pay $8.

a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. 

Probability Distribution Table

X P(X)
   
   
   

b. Find the expected profit. $ (Round to the nearest cent)

c. Interpret the expected value.

  • If you play many games, on average, you will likely win, or lose if negative, close to this amount.
  • You will win this much if you play a game.
  • This is the most likely amount of money you will win.
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Expert Answer

Step 1

a.

The possible outcomes when rolling a die is {1, 2, 3, 4, 5 and 6}.

The formula for finding probability of an event is shown below:

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Number of favorable outcomes Probability = Total number of outcomes

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Step 2

Using the given information, the probability distribution table is obtained as follows:

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х РХ) $8 1/6 $3 4/6 1/6 -$8

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Step 3

b)

The expected profit is obt...

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Expected profit XP(x) 1 $3 x--$8x- 6 1 = $8 x 6 6 - $2.5

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