Question

a. The probability that a ticket wins the main prize in a weekly lottery is 0.00001. For how many weeks do we need to participate in this lottery in order to win once in expected value?

b. In order to carry out a national health survey, the survey company uses the electoral roll that lists all households in the country. It selects a sample of households for the survey using random numbers to choose 0.1% of households from the electoral roll. What type of sampling is used?

Answer 1

a.) p : probability of winning main lottery prize in a week , p= 0.00001

n : number of weeks

X: Number of times lottery won in n weeks.

X~ Binomial(n,p)

E(X)=np=1

therefore n*0.00001=1

n=100000

b.) simple random sampling is used because each household has equal chance of being selected.