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.
It is 3yd (the Hight) x 4 yard(half the base) = 12yard and that is actually double the size of the single triangle we just measured but add its partner back on its:
12 YARD
Answer:
cos(71)
Step-by-step explanation:
Since 19° is less than 90, we can express this in terms of confunction.
sin(θ) = cos(90-θ)
sin(19) = cos(90-19)
sin(19) = cos(71)
Answer:
Ratio of triangle = 3 : 4
Step-by-step explanation:
Given:
Parallel sides = 9 cm , 12 cm
Find:
Ratio of triangle
Computation:
Assume height = h
Area of triangle = [1/2]bh
Area of triangle (1) = [1/2](9)h
Area of triangle (1) = 4.5 h
Area of triangle (2) = [1/2](12)h
Area of triangle (2) = 6 h
Ratio of triangle = 4.5 h / 6 h
Ratio of triangle = 3 : 4