I think it’s A I’m not sure though
Answer:
4^6
Step-by-step explanation:
Answer:
Answer is 0.64
Step-by-step explanation:
Given that pdf of x is
![f(x)={k(x−2),for 2≤x](https://tex.z-dn.net/?f=f%28x%29%3D%7Bk%28x%E2%88%922%29%2Cfor%202%E2%89%A4x%3C7%5C%5C%20f%28x%29%3D%7Bk%2812%E2%88%92x%29%2Cfor%207%E2%89%A4x%3C12)
Since total probability is 1 we can use this to find k.
![\int\limits^7_2 {k(x-2)} \, dx +\int\limits^12_7 {k(12-x)} \, dx \\=k\frac{(x-2)^2}{2} -k\frac{(12-x)^2}{2} \\=\frac{k}{2} [(7-2)^2-(2-2)^2-(12-12)^2+(7-12)^2]\\=\frac{k}{2}[25+25]=1\\k =\frac{1}{25}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E7_2%20%7Bk%28x-2%29%7D%20%5C%2C%20dx%20%2B%5Cint%5Climits%5E12_7%20%7Bk%2812-x%29%7D%20%5C%2C%20dx%20%5C%5C%3Dk%5Cfrac%7B%28x-2%29%5E2%7D%7B2%7D%20-k%5Cfrac%7B%2812-x%29%5E2%7D%7B2%7D%20%5C%5C%3D%5Cfrac%7Bk%7D%7B2%7D%20%5B%287-2%29%5E2-%282-2%29%5E2-%2812-12%29%5E2%2B%287-12%29%5E2%5D%5C%5C%3D%5Cfrac%7Bk%7D%7B2%7D%5B25%2B25%5D%3D1%5C%5Ck%20%3D%5Cfrac%7B1%7D%7B25%7D)
the probability that the fire loss is between 5 and 9=![P(5](https://tex.z-dn.net/?f=P%285%3Cx%3C9%29%3D%5Cint%5Climits%5E9_5%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5C%5C%3D%5Cint%5Climits%5E7_5%20%7Bf%28x%29%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E9_7%20%7Bf%28x%29%7D%20%5C%2C%20dx%5C%5C%3D%288%2B8%29%5Cfrac%7B1%7D%7B25%7D%20%5C%5C%3D0.64)
The chance of picking a almond cookie the first time:
you have 6 cookies, 3 of them are almond
So the chance of taking an almond cookie is
![\frac{3}{6} = \frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B6%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
The second time there are 5 cookies left, 2 of them are almond cookies
The chance of taking an almond cookie is
![\frac{2}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B5%7D%20)
To know the probability of picking two almond cookies in a row, multiply the changes:
![\frac{1}{2} \times \frac{2}{5} = \frac{1}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B5%7D%20)
The chance of taking two almond cookies is 1/5