White boxers are dogs that have a genetic disposition for going deaf within the

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 nine white boxer puppies contained two dogs that would eventually experience deafness. A family randomly selected two 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.

Explanation / Answer

a)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    9      
K = number of successes in the population =    2      
n = sample size =    2      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.583333333 [ANSWER]

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b)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    9      
K = number of successes in the population =    2      
n = sample size =    2      
x = number of successes in the sample =    1      
          
Thus,          
          
P(   1   ) =    0.388888889 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    9      
K = number of successes in the population =    2      
n = sample size =    2      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) =    0.027777778 [ANSWER]

********************

d)

Mean = nK/N = 2*(2/9) = 0.444444444 [ANSWER]

standard deviation = sqrt[(nK(N-K)(N-n))/(N^2 (N-1))] = sqrt((2*2*(9-2)*(9-2))/(9^2*(9-1)))

standard deviation = 0.549971941 [ANSWER]

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