Answer to Question #346481 in Statistics and Probability for shiba

Question

According to a genetics theory,a certain cross of guinea pigs will result in red,black, and white offspring in the ratio 8:4:4.Find the probability that among 8 offspring,5 will be red,2 black, and 1 white.

Answer 1

$$P(red)=\dfrac{8}{8+4+4}=\dfrac{1}{2}$$

$$P(black)=\dfrac{4}{8+4+4}=\dfrac{1}{4}$$

$$P(white)=\dfrac{4}{8+4+4}=\dfrac{1}{4}$$

If a random variable X follows a multinomial distribution

$$P(5red\ \&\ 2black\ \ \&\ 1white)$$

$$=8!(\dfrac{1}{2})^5(\dfrac{1}{4})^2(\dfrac{1}{4})(\dfrac{1}{5!})(\dfrac{1}{2!})(\dfrac{1}{1!})$$

$$=\dfrac{21}{256}\approx0.082031$$