Question

White boxers are dogs that have a genetic disposition for going deaf within the first year after they are born. Suppose a litter of seven white boxer puppies contained two dogs that would eventually experience deafness. A family randomly selected three puppies from this litter to take home as family pets. (For this problem, define a success as selecting a dog that will eventually experience deafness.) Complete parts a through d below. (round all answers to four decimal places)

a. Determine the probability that none of the two puppies selected will experience deafness.

b. Determine the probability that one of the two puppies selected will experience deafness.

c. Determine the probability that both puppies selected will experience deafness.

d. Calculate the mean and standard deviation of this distribution.

Answer 1

The probabbility that white boxer puppies will experience deafness is p = 2/7 = 0.2857

The number of puppies selected by the family from this litter is n = 3

Let X be the number of puppies selected will experience deafness.

X ~ Binomial( 3, 0.2857 )

The probability mass function for x puppies from n=3 puppies will experience deafness is given as:

a) The probability that none of the two puppies selected will experience deafness is

b) The probability that one of the two puppies selected will experience deafness is

c) The probability that both puppies selected will experience deafness is

d)

Mean = np = 3*0.2857 = 0.8571

Variance = np(1-p) = 3*0.2857*(1-0.2857) = 0.6122

Standard deviation = 0.7824