In cocker spaniels, solid coat color is dominant over spotted coat color. Suppose a homozygous solid-colored dog is crossed to a spotted dog and the F1 are crossed with each other. If three F2 puppies are born, what is the probability that at least one of the three puppies will have a spotted coat

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Answer:

0.5781

Step-by-step explanation:

Let 'S' be the dominant allele for solid coat color and 's' be the recessive allele for spotted coat color.

By crossing a homozygous solid-colored dog (SS) with a spotted dog (ss), all of the F1 will present the Ss genotype.

When crossing two F1 dogs, the sample space for F2 is:

F2={Ss,sS,ss,SS}

For each puppy, there is a 1 in 4 chance of having a spotted coat.

The probability that at least one of the three F2 puppies have a spotted coat is 100% minus the probability that none have a spotted coat:

[tex]P(ss>0) =1- P(ss=0)\\P(ss>0) =1- (1-\frac{1}{4} )^3\\P(ss>0) = 0.5781[/tex]

The probability that at least one of the three F2 puppies will have a spotted coat is 0.5781.