A game of chance involves rolling a standard, six-sided die. The amount of money the player wins depends on the result of the die roll: * If the result is 1 or 2, the player wins nothing; * If the result is 3, 4, or 5, the player wins 4 dollars; * If the result is 6, the player wins 36 dollars. (Note: Your answer to the question below should be rounded to three decimal places.) If you play this game once (and it costs you nothing to play), what is the expected amount of money you will win?

Answer:

If you play this game once (and it costs you nothing to play), the expected amount of money you will win is:

$8.

Step-by-step explanation:

a) Data and Calculations:

The probability for the result to be 1 or 2 = 33.33% (100/6 * 2)

The probability for the result to be 3, 4, or 5 = 50% (100/6 * 3)

The probability for the result to be 6 = 16.67% (100/6 * 1)

Data Table:

Event                              Probability       Value Won

The result is 1 or 2           33.33%              $0

The result is 3, 4 or 5     50.00%              $4.00

The result is 6                 16.67%              $36.00

Expected Value:

Event                              Probability          Value              Expected Value

The result is 1 or 2           33.33%              $0                $0 ($0 * 33.33%)

The result is 3, 4 or 5     50.00%              $4.00           $2.00 ($4 * 50%)

The result is 6                 16.67%              $36.00          $6.00 ($36 * 16.67%)

Total expected amount of money  =                             $8.00

Final answer:

The expected win from playing the game once is $8. This is calculated by finding the expected value of the winnings, which is the sum of the possible outcomes each multiplied by their probabilities.

Explanation:

This question is asking about the expected amount of money one can win in a game involving a six-sided die. The concept of 'expectation' in probability and statistics refers to the average result of an experiment if it were repeated many times.

In our game, the possible outcomes when you roll the die are $0 (when we roll 1 or 2), $4 (when we roll 3, 4 or 5), and $36 (when we roll a 6). Now, to calculate the expected value, or the expected amount of money one would win in this game, we multiply each possible outcome by their probability and sum them up.

We have a 1/3 chance of winning $0, a 1/2 chance of winning $4, and a 1/6 chance of winning $36. Therefore, the expected value of winnings would be:

(1/3 * $0) + (1/2 * $4) + (1/6 * $36) = $0 + $2 + $6 = $8

Therefore, if you play this game once, the expected amount of money you will win is $8.

Learn more about Expected Value here:

brainly.com/question/37190983

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