Question

Clinical studies of 1,000 people were analyzed to determine if they have a gene that predisposes people to skin cancer. That study revealed that the probability that a person has the gene predisposed to contract cancer is 01.
a) Calculate the probability that 4 or more people will have to be tested before two people are detected with the gene.
b) On average, how many people must be analyzed for 2 people to be detected with the gene.

Answer 1

We are given here the probability that a person has the required gene that contracts cancer to be 0.1.

a) The probability that 4 or more people are to be tested before 2 of them are detected with the required gene is computed here as:

= 1 - Probability that the first 3 persons tested have 2 or 3 people with required gene

= 1 - 3*0.12*(1 - 0.1) - 0.13 = 0.972

therefore 0.972 is the required probability here.

b) This is a case of a sum of 2 geometric progressions, The mean of a geometric progression is 1/p

Therefore On average, number of people that must be analyzed for 2 people to be detected with the gene is computed here as:

= 2/p

= 2/0.1

= 20

therefore 20 people is the required number of people to be tested here.