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

Answer: \($1.17\)



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


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

 Jul 18, 2021


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