Answer:
Step-by-step explanation:
The main idea is that I would like to pay less than what I'm expecting to win, so in that way, I get a profit out of playing this game. Let X be the number of tosses until I get a Heads. By definition, this is a geometric random variable with parameter p = 1/2.
Let Y the amount I received for playing. So, we want to calculate the expected value of Y.
We can calculate it as follows
![E[Y] = 2 P(X=1)+ 4 P(X=2)+ 8 P(X =3) + \dots = \sum_{n=1}^infty 2^n P(X=n)](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%202%20P%28X%3D1%29%2B%204%20P%28X%3D2%29%2B%208%20P%28X%20%3D3%29%20%20%2B%20%5Cdots%20%20%3D%20%5Csum_%7Bn%3D1%7D%5Einfty%202%5En%20P%28X%3Dn%29)
Since X is a geometric random variable, we have that 
Then,
![E[Y] = \sum_{n=1}^\infty 2^{n} (\frac{1}{2})^{n-1} \frac{1}{2} = \sum_{n=1}^\infty 2^{n-1} \cdot \frac{1}{2^{n-1}} = \sum_{n=1}^\infty 1 = \infty](https://tex.z-dn.net/?f=%20E%5BY%5D%20%3D%20%5Csum_%7Bn%3D1%7D%5E%5Cinfty%202%5E%7Bn%7D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Csum_%7Bn%3D1%7D%5E%5Cinfty%202%5E%7Bn-1%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7B2%5E%7Bn-1%7D%7D%20%3D%20%5Csum_%7Bn%3D1%7D%5E%5Cinfty%201%20%3D%20%5Cinfty)
So, we expect to have an infinite amount. Given this, we can pay as much as we want to play the game.
Answer: x=2.5, and x-1=1.5
Step-by-step explanation:
x + 3 = 3x - 1
(-x)= 3 = 2x - 1
(÷2) = 1.5 = x - 1
(+1)= 2.5 = x
Answer:130
Step-by-step explanation:
Answer: 8.75$
Step-by-step explanation: to find the answer to this problem, you would divide his total amount of cash earned by the number of hours he worked to see how the cash is split between each hour. By doing this, you should get 8.75$ and hour.
X= purchase price
Multiply purchase price by sales tax % to equal the amount of sales tax.
(8.75% * x)= $15.75
convert % to decimal (8.75% ÷ 100)
0.0875x= 15.75
divide both sides by 0.0875
x= $180.00 purchase price
ANSWER: The purchase price is $180.00 (to nearest cent).
Hope this helps! :)
