It is estimated that 57.9 percent of eligible Americans voted in the last presidential election. You decide to ask 8 eligible voters if they voted.

Question

Using binomial or geometric models, find the probability of the following:

a) At least 1 person voted this year

Answer 1

If you calculate the probability of at least 1, you'd have to calculate P(1), P(2), P(3), ..., and P(8) and then add them up.

A different and easier approach is to remember that the complement of at least 1 is none, so if you calculate P(none) first, you can easily find P(at least 1) by using 1 - P(none).

If 57.9% voted, then 42.1% did not vote. So P(None) = (0.421)^8 ≈ 0.000986.

Therfore, P(at least 1) ≈ 1 - 0.000986 = 0.999014