Let
be the random variable representing the winnings you get for playing the game. Then
![W=\begin{cases}9&\text{if the sum is odd}\\4&\text{if the sum is 4 or 8}\\49&\text{if the sum is 2 or 12}\\-1&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=W%3D%5Cbegin%7Bcases%7D9%26%5Ctext%7Bif%20the%20sum%20is%20odd%7D%5C%5C4%26%5Ctext%7Bif%20the%20sum%20is%204%20or%208%7D%5C%5C49%26%5Ctext%7Bif%20the%20sum%20is%202%20or%2012%7D%5C%5C-1%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
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
![P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=P%28W%3Dw%29%3D%5Cbegin%7Bcases%7D%5Cfrac12%26%5Ctext%7Bfor%20%7Dw%3D9%5C%5C%5Cfrac29%26%5Ctext%7Bfor%20%7Dw%3D4%5Ctext%7B%20or%20%7Dw%3D-1%5C%5C%5Cfrac1%7B18%7D%26%5Ctext%7Bfor%20%7Dw%3D49%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
The expected value of playing the game is then
![E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{71}9](https://tex.z-dn.net/?f=E%5BW%5D%3D%5Cdisplaystyle%5Csum_ww%5C%2CP%28W%3Dw%29%3D%5Cfrac%7B71%7D9)
or about $7.89.
The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.
Answer:
2.72 ml
Step-by-step explanation:
4 lb = 1814.37 gm
1814.37 gm * .09 mg/gm / ( 60 mg/ml) = 2.72 ml
Answer:
e
Step-by-step explanation:
Answer:4
Step-by-step explanation: look at the image attached