Respuesta :
Answer:
The probability that among 12 offspring, 6 will be red, 3 black and 3 white will be ≅ 0.058
Explanation:
A certain cross of guinea pigs will result in red, black, and white offspring in the ratio 9:5:4
Red
p1 = [tex]\frac{9}{9 + 5 + 4} = 0.5[/tex]
Black
p2 = [tex]\frac{5}{9 + 5 + 4} = 0.28[/tex]
White
p3 = [tex]\frac{4}{9 + 5 + 4} = 0.22[/tex]
Find the probability that among 12 offspring, 6 will be red, 3 black and 3 white
x1, x2, x3 = represent the number of red, black and white offspring among 12
n = 12 (independent trials) --> each trial can result in 3 outcomes (red, black, and white) with probabilities of p1 = 0.5; p2 = 0.28; p3 = 0.22
Applying the multinomial distribution
f(x1, x2, x3; p1, p2, p3, n) = (n x1, x2, x3) [tex]p1^{x2} p2^{x2} p3^{x3}[/tex]
Find the probability of x1 = 6, x2 = 3, x3 = 3
f(6, 3, 3; 0.5, 0.28, 0.22, 12) = (12 6, 3, 3) [tex]0.5^{6} 0.28^{3} 0.22^{3}[/tex]
= [tex](\frac{12!}{6! 3! 3!})[/tex] 0.015 * 0.021 * 0.010
= 18480 (0.015 * 0.021 * 0.010)
≅ 0.058
The probability that among 12 offspring, 6 will be red, 3 black and 3 white will be ≅ 0.058
A certain cross of guinea pigs will result in red, black, and white offspring in the ratio 9:5:4
Red
p1 = [tex]\frac{9}{9+5+4} =0.5[/tex]
Black
p2 = [tex]\frac{5}{9+5+4} =0.28[/tex]
White
p3 = [tex]\frac{4}{9+5+4}=0.22[/tex]
Find the probability that among 12 offspring, 6 will be red, 3 black, and 3 white
x1, x2, x3 = represent the number of red, black, and white offspring among 12
n = 12 (independent trials) --> each trial can result in 3 outcomes (red, black, and white) with probabilities of p1 = 0.5; p2 = 0.28; p3 = 0.22
Applying the multinomial distribution
f(x1, x2, x3; p1, p2, p3, n) = (n x1, x2, x3) [tex]p1^{x2} p2^{x2} p3^{x3}[/tex]
Find the probability of x1 = 6, x2 = 3, x3 = 3
f(6, 3, 3; 0.5, 0.28, 0.22, 12) = (12 6, 3, 3) [tex]0.5^{6 } 0.28^{3} 0.22^{3}[/tex]
= 0.015 * 0.021 * 0.010
= 18480 (0.015 * 0.021 * 0.010)
≅ 0.058
Thus, the probability among 12offspring, 6 will be red, 3 black, and 3 white here.
Learn more about the genetics theory of guinea pigs here:
https://brainly.com/question/505001
