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.

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 =

Black

p2 =

White

p3 =

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)

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)

                                              = 0.015 * 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 =

Black

p2 =

White

p3 =

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)

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)

                                             =  0.015 * 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: