A population of 900 voters contains 369 Republicans, 468 Democrats, and 63 indep

Question

A population of 900 voters contains 369 Republicans, 468 Democrats, and 63 independents and members of other parties. A simple random sample of 90 voters will be drawn from this population.

The expected value of the number of Republicans in the sample is? (Q)____________

The chance the sample contains only Republicans and Democrats is? (Q)___________

Consider repeatedly drawing simple random samples of size 90 from the population (taking each simple random sample from the full population of 900 voters). The expected value of the number of simple random samples of size 90 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? (Q)_____________

Explanation / Answer

1) Expected value of the number of Republicans in the sample is (90/900) * 369 = 36.9

For the purpose of checking it, 32 Democrats and 5 otherwise yields.

2) chance the sample contains only Republicans and Democrats is

= ((369+468) / 900 ))^90 =0.00145

The (369+468) is the number of Republican + the number of Democrats. The 900 is the total population. The 90 s the number of selections

3) For the first pick the probability is 1 - ((9/10)^90) = 0.99855 (1 - "the answer to 2")

This is true for all subsequent picks, but that's irrelevant.

While it is true that all picks could be only Democrats and Republicans, it's close to impossible. So it is possible that no such pick occurs but infinitely unlikely.

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