Question

statistics show that about 42% of americans voted in the previous national election. if three americans are randomly selected, what is the probability that none of them voted in the last election?
0.07
0.42
0.58
0.93
0.20

Explanation:

Step1: Find probability of not - voting

The probability that an American voted is $p = 0.42$. So the probability that an American did not vote is $q=1 - p=1 - 0.42 = 0.58$.

Step2: Use multiplication rule for independent events

Since the selection of each American is an independent event, the probability that none of the three randomly - selected Americans voted is $q\times q\times q=q^{3}$.
Substitute $q = 0.58$ into the formula: $0.58\times0.58\times0.58=0.58^{3}=0.195112\approx0.20$.

Answer:

E. 0.20