Find the indicated probability.

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?

To solve this problem, we can use the concept of probability involving independent events.

Let:
- \( p = 0.42 \) be the probability that an American voted in the last election.
- The probability that an American did not vote in the last election is \( 1 - p = 1 - 0.42 = 0.58 \).

Since we are selecting three Americans independently, the probability that none of them voted is the product of the probability that each individual did not vote:

\[
P(\text{none voted}) = 0.58 \times 0.58 \times 0.58 = 0.58^3
\]

Now, let's calculate this:

\[
0.58^3 \approx 0.1951
\]

So, the probability that none of the three randomly selected Americans voted in the last election is approximately 0.1951 or 19.51%.

Would you like more details, or do you have any questions? Here are some related questions you might find interesting:

1. What is the probability that at least one of the three selected Americans voted in the last election?
2. How does the probability change if four Americans are selected instead of three?
3. What is the probability that exactly one out of the three Americans voted?
4. How would you calculate the probability if the voting rate was different, say 50%?
5. How does the assumption of independence affect this probability calculation?

**Tip:** When dealing with independent events, the probability of all events occurring is the product of their individual probabilities.

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?

Calculate the probability that none of three randomly selected Americans voted in the last election using probability concepts. Explore key formulas like P(None Voted) = (1 - p)^n and learn how to solve probability problems with independent events. Suitable for Grades 9-12.

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