Biology, 14.02.2020 22:25 epmooneyham7372

According to a genetics theory, a certain cross of guinea pigs will result in red, black, and white offspring in the ratio 9:5:4. Find the probability that among 12 offspring, 6 will be red, 3 black and 3 white.

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Answer from: FireFlight

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 = $\frac{9}{9 + 5 + 4} = 0.5$

Black

p2 = $\frac{5}{9 + 5 + 4} = 0.28$

White

p3 = $\frac{4}{9 + 5 + 4} = 0.22$

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) $p1^{x2} p2^{x2} p3^{x3}$

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) $0.5^{6} 0.28^{3} 0.22^{3}$

= $(\frac{12!}{6! 3! 3!})$ 0.015 * 0.021 * 0.010

= 18480 (0.015 * 0.021 * 0.010)

≅ 0.058

Answer from: AskaWaya

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 = $\frac{9}{9+5+4} =0.5$

Black

p2 = $\frac{5}{9+5+4} =0.28$

White

p3 = $\frac{4}{9+5+4}=0.22$

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) $p1^{x2} p2^{x2} p3^{x3}$

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) $0.5^{6 } 0.28^{3} 0.22^{3}$

= 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:

Answer from: Quest

That statement is true.

Answer from: Quest

human didn't come from monkeys man i hate these stupid teachers

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