Question

Mad cow disease is a serious health concern in cattle from Alberta, Canada. If 5 cattle in a herd of 40 are infected and 10 cattle are chosen at random for testing, find the following probabilities:

a. None of the sample cattle have mad cow disease.

b. At least one of the sample cattle has mad cow disease.

c. Two of the sample cattle have mad cow disease.

Answer 1

a) Probability that none of the sample cattle have mad cow disease is computed here as:

= Number of ways to select 10 cows from 35 non infected cattle / Number of ways to select 10 cows from the 40 cattle

Therefore 0.2166 is the required probability here.

b) Probability that at least one of the sample cattle has mad cow disease is computed here as:

= 1 - Probability that none of the sample cattle have mad cow disease

= 1 - 0.2166

= 0.7834

Therefore 0.7834 is the required probability here.

c) Probability that two of the sample cattle have the disease is computed here as:

= Number of ways to select 2 cows from the 5 infected cattle * Number of ways to select rest 8 cattle from the 35 non infected cattle / Number of ways to select 10 cows from the 40 cattle

Therefore 0.2777 is the required probability here.