Question

Wavy hair in mice is a recessive genetic trait. if mice with wavy hair are mated with straight-haired (heterozygous) mice, each offspring has probability 1 2 of having wavy hair.29 consider a large number of such matings, each producing a litter of five offspring. what percentage of the litters will consist of (a) two wavy-haired and three straight-haired offspring?

Answer 1

To calculate the percentage of litters with two wavy-haired and three straight-haired mice, the binomial probability formula is used, resulting in a 31.25% chance.

Step-by-step explanation:

Wavy hair in mice is a recessive genetic trait. If wavy-haired mice are mated with heterozygous straight-haired mice, each offspring has a 1/2 probability of inheriting wavy hair. When dealing with a large number of matings, where each produces a litter of five offspring, we can calculate the percentage of litters consisting of two wavy-haired and three straight-haired offspring.

To solve this, we use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where:

• n = total number of offspring (5)
• k = number of wavy-haired offspring desired (2)
• p = probability of wavy hair (1/2)

Plugging in the numbers:

P(2 wavy, 3 straight) = (5 choose 2) * (1/2)^2 * (1/2)^(5-2) = 10 * 1/4 * 1/8 = 10/32 = 31.25%

Therefore, the percentage of litters with exactly two wavy-haired and three straight-haired mice is 31.25%.

Answer 2

In order to find the percentage of the litters that will consist of two wavy- haired and three straight-haired offspring, you need to use the binomial distribution formula: P(x) = ⁿCₓ × pₓ × qⁿ⁻ˣ

P is the probability that the litters will consist of two wavy-haired and three straight-haired offspring.

X is considered to be the number of times the offspring will have wavy-air in a litter of 5 offspring, which is 2.

n is the number of offspring per litter.

p is the probability of happening wavy hair.

q is the probability of having straight hair.

It comes like this:

P(X=2)=⁵C₂×0.5²×0.5⁵⁻² ⇔ P(X=2)=10×0.25×0.125 ⇔ P(X=2)=0.3125

So, the percentage of the litters that will consist of two wavy-haired and three straight-haired offspring is 31.25%.