You have been hired for the summer by a dog breeder. He is excited to have a gen

Question

You have been hired for the summer by a dog breeder. He is excited to have a genetics student working with him as his livelihood depends on producing Labrador puppies of a certain colour! Black Labrador puppies can fetch up to $500, whereas golden Labrador puppies can only fetch up to $250. Assume that the probability that a black puppy will be born is ½, and that the probability that a golden puppy will be born is ½.

(a) If a dog gives birth to seven puppies, what is the probability that all seven puppies will be black? Show your calculations.

(b) What is the probability that, in a litter of five puppies, the first puppy will be black, the second puppy will be black, the third puppy will be golden, the fourth puppy will be black and the fifth puppy will be black? Show your calculations.

(c) What is the probability that a litter of four puppies will either be all black, or all golden? Show your calculations.

Explanation / Answer

a) probability that all seven puppies will be black =(1/2)7 =0.0078

b) probability that, in a litter of five puppies, the first puppy will be black, the second puppy will be black, the third puppy will be golden, the fourth puppy will be black and the fifth puppy will be black=P(BBGBB)=(1/2)*(1/2)*(1/2)*(1/2)*(1/2) =0.03125

c)  probability that a litter of four puppies will either be all black, or all golden =P( all golden +all black)

=(1/2)4+(1/2)4 =0.125

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