Question

1. joe is playing a game with a regular die. if the number that turns up is even, he will gain 5 times the number that comes up. if it is odd, he will lose 10 times the number that comes up. he tosses a 3. express the results as an integer.

Explanation:

Step1: Determine gain from even - numbered results

The probability of getting an even number on a regular die is $\frac{3}{6}=\frac{1}{2}$. He gains 5 times the number that comes up when it's even. The possible even numbers are 2, 4, 6. The expected value of an even - numbered roll is $\frac{2 + 4+6}{3}=4$. So the gain from even - numbered results is $5\times4 = 20$.

Step2: Determine gain/loss from odd - numbered results

The probability of getting an odd number on a regular die is $\frac{3}{6}=\frac{1}{2}$. He loses 10 times the number that comes up when it's odd. The possible odd numbers are 1, 3, 5. The expected value of an odd - numbered roll is $\frac{1 + 3+5}{3}=3$. So the loss from odd - numbered results is $10\times3=30$.

Step3: Calculate the net result

The net result is the gain from even - numbered results minus the loss from odd - numbered results. Net result=$20-30=- 10$.

Answer:

-10