Answer:
12.5 lb of Brand A and 37.5 lb of Brand B
Step-by-step explanation:
Let a = weight of Brand A.
Let b = weight of Brand B.
To make 50 lb of bird seed, we get the equation:
a + b = 50
Now we deal with the amount of sunflower seed in each Brand and in the final mixture.
a amount of Brand A has 0.2a amount of sunflower seed.
b amount of Brand B has 0.6b amount of sunflower seed.
50 lb of the mixture has 0.5 × 50 lb = 25 lb of sunflower seed.
That gives us the second equation.
0.2a + 0.6b = 25
We have a system of equations:
a + b = 50
0.2a + 0.6b = 25
Solve the first equation for a and substitute in the second equation.
a = 50 - b
0.2(50 - b) + 0.6b = 25
10 - 0.2b + 0.6b = 25
0.4b + 10 = 25
0.4b = 15
b = 37.5
Now substitute 37.5 for b in the first original equation and solve for a.
a + 37.5 = 50
a = 12.5
12.5 lb of Brand A and 37.5 lb of Brand B
14 * 9000
---
9
126000
-----------
9
=14000
Answer:
The probability that the animal chosen is brown-haired is 0.6333.
Step-by-step explanation:
Denote the events as follows:
<em>A</em> : a brown-haired rodent
<em>B</em> : Litter 1
The information provided is:
![P (A|B) =\frac{2}{3}\\\\P(A|B^{c})=\frac{3}{5}](https://tex.z-dn.net/?f=P%20%28A%7CB%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5CP%28A%7CB%5E%7Bc%7D%29%3D%5Cfrac%7B3%7D%7B5%7D)
The probability of selecting any of the two litters is equal, i.e.
![P(B)=P(B^{c})=\frac{1}{2}](https://tex.z-dn.net/?f=P%28B%29%3DP%28B%5E%7Bc%7D%29%3D%5Cfrac%7B1%7D%7B2%7D)
According to the law of total probability:
![P(X)=P(X|Y_{1})P(Y_{1})+P(X|Y_{2})P(Y_{2})+...+P(X|Y_{n})P(Y_{n})](https://tex.z-dn.net/?f=P%28X%29%3DP%28X%7CY_%7B1%7D%29P%28Y_%7B1%7D%29%2BP%28X%7CY_%7B2%7D%29P%28Y_%7B2%7D%29%2B...%2BP%28X%7CY_%7Bn%7D%29P%28Y_%7Bn%7D%29)
Compute the total probability of event <em>A</em> as follows:
![P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})](https://tex.z-dn.net/?f=P%28A%29%3DP%28A%7CB%29P%28B%29%2BP%28A%7CB%5E%7Bc%7D%29P%28B%5E%7Bc%7D%29)
![=[\frac{2}{3}\times\frac{1}{2}]+[\frac{3}{5}\times\frac{1}{2}]\\\\=\frac{1}{3}+\frac{3}{10}\\\\=\frac{10+9}{30}\\\\=\frac{19}{30}\\\\=0.6333](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B2%7D%7B3%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%5D%2B%5B%5Cfrac%7B3%7D%7B5%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%5D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B3%7D%7B10%7D%5C%5C%5C%5C%3D%5Cfrac%7B10%2B9%7D%7B30%7D%5C%5C%5C%5C%3D%5Cfrac%7B19%7D%7B30%7D%5C%5C%5C%5C%3D0.6333)
Thus, the probability that the animal chosen is brown-haired is 0.6333.