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.
+307 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 \($1.17\).
