Question

1) Clinical studies of 1000 people were analyzed to determine if they have a gene that predisposes people to have skin cancer. That study revealed that the probability that a person has the gene predisposed to contract cancer is 0.1. a) Calculate the probability that 4 or more people have to be analyzed before two people are detected with the gene. bi on average, how many people must be analyzed for 2 people to be detected? with the gene.

Answer 1

a)

P(4 or more to be analysed to get 2 people with gene) =1-P(At most 1 wtih gene in first 3)

=1-P(X=0)-P(X=1)\

1-(3C0)*0.1^0*0.9^3-(3C1)*0.1^1*0.9^2

=0.9720

b)

here this follows negative binomial distribution with parameter r =2 and p=0.1

expected number =r/p=2/0.1 =20