3) Mendelian genetics predict that in Labrador retrievers (a type of dog), 25% s

Question

3) Mendelian genetics predict that in Labrador retrievers (a type of dog), 25% should have brown coat color if both parents are heterozygous (the rest are black). You mate two parents and get

a litter of 6 puppies. Calculate the following:

a) The probability of 4 brown puppies. b) The probability of 3 brown puppies. c) The probability that 50% of the puppies will be brown.

Refer to problem 3. Suppose you now have a litter of 2 puppies. Calculate the probability of every possible outcome (hint: you need to make three calculations).

Explanation / Answer

This will be a binomial distribution with parameters:

n = 6, p = 0.25

q = 1 - p = 1 - 0.25 = 0.75

a) P(X = 4) = 6C4 (0.25)4(0.75)2 = 0.0330

b) P(X = 3) = 6C3 (0.25)3(0.75)3 = 0.1318

c) P(50% puppies will be brown) = P(X = 6/2) = P(X = 3) = 0.1318

Now if we have two puppies then number of brown puppies can either be 0, 1 or 2.

So,

Probability of every outcome will be:

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