Answer:
The probability that the animal chosen is brown-haired is 0.6333.
Step-by-step explanation:
Denote the events as follows:
A : a brown-haired rodent
B : Litter 1
The information provided is:
[tex]P (A|B) =\frac{2}{3}\\\\P(A|B^{c})=\frac{3}{5}[/tex]
The probability of selecting any of the two litters is equal, i.e.
[tex]P(B)=P(B^{c})=\frac{1}{2}[/tex]
According to the law of total probability:
[tex]P(X)=P(X|Y_{1})P(Y_{1})+P(X|Y_{2})P(Y_{2})+...+P(X|Y_{n})P(Y_{n})[/tex]
Compute the total probability of event A as follows:
[tex]P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})[/tex]
[tex]=[\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[/tex]
Thus, the probability that the animal chosen is brown-haired is 0.6333.
