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.
My work:
1: no (-3)
2: yes (+2)
3: yes (+3)
4: no (-3)
5: yes (+5)
6: no (-3)
this adds up to 10-9=1. What now?
+770 yeah, you're on the right track! so, there's a 1/6 probability of rolling a 1 (and losing 3 bucks), a 1/3 probability of rolling a composite (and winning/losing 0), and a 1/6 probability of winning each of 2, 3, and 5.
So... the expected value would just be \(\dfrac{1}{3} \cdot \$0 + \dfrac{1}{6} \cdot (\$2+\$3+\$5) + \dfrac{1}{6} \times -\$3 \approx \boxed{1.17}.\)
hey, that's pretty good!
