Answer to Question #346481 in Statistics and Probability for shiba

Question #346481

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.


1
Expert's answer
2022-05-31T13:56:41-0400
P(red)=88+4+4=12P(red)=\dfrac{8}{8+4+4}=\dfrac{1}{2}

P(black)=48+4+4=14P(black)=\dfrac{4}{8+4+4}=\dfrac{1}{4}

P(white)=48+4+4=14P(white)=\dfrac{4}{8+4+4}=\dfrac{1}{4}

If a random variable X follows a multinomial distribution

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

=8!(12)5(14)2(14)(15!)(12!)(11!)=8!(\dfrac{1}{2})^5(\dfrac{1}{4})^2(\dfrac{1}{4})(\dfrac{1}{5!})(\dfrac{1}{2!})(\dfrac{1}{1!})

=212560.082031=\dfrac{21}{256}\approx0.082031


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