Let
be the random variable representing the winnings you get for playing the game. Then

First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.
- The sum is odd if one die is even and the other is odd. This can happen 2 * 3 * 3 = 18 ways. (3 ways to roll even with the first die, 3 ways to roll odd for the die, then multiply by 2 to count odd/even rolls)
- The sum is 4 if you roll (1, 3), (2, 2), or (3, 1), and the sum is 8 if you roll (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2). 8 ways.
- The sum is 2 if you roll (1, 1), and the sum is 12 if you roll (6, 6). 2 ways.
- There are 36 total possible rolls, from which you subtract the 18 that yield a sum that is odd and the other 10 listed above, leaving 8 ways to win nothing.
So the probability mass function for this game is

The expected value of playing the game is then
![E[W]=\displaystyle\sum_ww\,P(W=w)=\frac92+\frac89-\frac29+\frac{49}{18}=\frac{71}9](https://tex.z-dn.net/?f=E%5BW%5D%3D%5Cdisplaystyle%5Csum_ww%5C%2CP%28W%3Dw%29%3D%5Cfrac92%2B%5Cfrac89-%5Cfrac29%2B%5Cfrac%7B49%7D%7B18%7D%3D%5Cfrac%7B71%7D9)
or about $7.89.
Answer:
recess is at 10:00
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
![4a+7\\\\a=\frac{1}{2}\\\\=4[\frac{1}{2}]+7\\\\=2+7\\\\=9](https://tex.z-dn.net/?f=4a%2B7%5C%5C%5C%5Ca%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%3D4%5B%5Cfrac%7B1%7D%7B2%7D%5D%2B7%5C%5C%5C%5C%3D2%2B7%5C%5C%5C%5C%3D9)
Answer:

Step-by-step explanation:
The solid that you described is shown in the image of below. To compute the volume we use triple integrals. Observe that



So, the volumen of the solid is given by

This last integral equals 