Question

Approximately 10.3% of American high school students drop out of school before graduation. Choose 10 students entering high school at random. Find the probability that all 10 stay in school and graduate. Round your answer to the nearest thousandth.

Answer 1

To find the probability that all 10 students stay in school and graduate, we first need to determine the probability that a single student does not drop out. Given that 10.3% of students drop out, the probability of a student staying in school and graduating is:

\[
P(\text{stay}) = 1 - P(\text{dropout}) = 1 - 0.103 = 0.897
\]

Now, since we want to find the probability that all 10 students stay in school, we can calculate that by raising the probability of one student staying in school to the 10th power:

\[
P(\text{all 10 stay}) = P(\text{stay})^{10} = (0.897)^{10}
\]

Now, we need to compute \(0.897^{10}\):

\[
0.897^{10} \approx 0.3487
\]

Finally, we round this answer to the nearest thousandth:

\[
P(\text{all 10 stay}) \approx 0.349
\]

Therefore, the probability that all 10 students stay in school and graduate is approximately **0.349**.