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Monica tosses a fair 6-sided die. If the roll is a prime number, then she wins that amount of dollars (so that, for example, if she rolls 3, then she wins 3 dollars). If the roll is composite, she wins nothing. Otherwise, she loses 3 dollars. What is the expected value of her winnings on one die toss? Express your answer as a dollar value to the nearest cent.

Jul 17, 2021

#1
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Answer: $$1.17$$

Solution:

Case 1: Monica rolls a 1.

If Monica rolls a 1, then she loses 3 dollars.

Case 2: Monica rolls a 2.

If Monica rolls a 2, then she gains 2 dollars.

Case 3: Monica rolls a 3.

If Monica rolls a 3, then she gains 3 dollars.

Case 4: Monica rolls a 4.

If Monica rolls a 4, then she gains nothing.

Case 5: Monica rolls a 5.

If Monica rolls a 5, then she gains 5 dollars.

Case 6: Monica rolls a 6.

If Monica rolls a 6, then she gains nothing.

Adding all them up and then placing it over six (there are six possibillities) gives

$$-3+2+3+0+5+0\over6$$

Which is equal to $$\frac76$$, which rounded to the nearest cent, gives $$1.17$$.

Jul 18, 2021