Question

A population of 1000 voters contains 330 Republicans, 620 Democrats, and 50 independents and members of other parties. A simple random sample of 100 voters will be drawn from this population. Consider repeatedly drawing simple random samples of size 100 from the population (taking each simple random sample from the full population of 1000 voters). The expected value of the number of simple random samples of size 100 that must be drawn until (and including) the first sample that contains at least one voter who is neither a Democrat nor a Republican is (Q7)

Answer 1

5

Explanation:

number of republican voters =330

number of democratic voters =620

number of independent voters =50

the chance that the sample contains only republican and democrats is

P( Republican and democrats )=P ( republican )+P(democrats )

=
`(330)/(1000)+(620)/(1000)=0.33+0.62=0.95`

the probability that neither a republican nor a democrats is =1-0.95=0.05

for expected value we have to multiply with n

so expected value =np=100×0.05=5