Question

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 4 puppies. Calculate the following: a) The probability of 4 black puppies. b) The probability of 2 brown puppies. c) The probability that 50% of the puppies will be brown. 4) Refer to problem 3. Calculate the probability of every possible outcome (hint: you need to make five calculations).

Answer 1

Solution:

This will be a binomial distribution with parameters:

n = 4, p = 0.25

q = 1 - p = 1 - 0.25 = 0.75

a) The probability of 4 black puppies means brown puppy is zero .

P(X = 0) = ⁴C₀ (0.25)⁰(0.75)⁴ = 0.3164

b) P(X = 2) = ⁴C₂ (0.25)²(0.75)² = 0.2109

c) P(50% puppies will be brown) = P(X = 4/2) = P(X = 2) = 0.2109

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

So,

Probability of every outcome will be:

x	0	1	2
p(x)	(0.75)2 = 0.5625	2*(0.25)*(0.75) = 0.375	(0.25)2 = 0.0625

Cheers!!

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