Question

It is reported that 77% of workers aged 16 and over drive to work alone. Choose 8 workers at random. Find the probability that all drive to work alone. Round your answer to the nearest thousandths.

Answer 1

To find the probability that all 8 randomly chosen workers drive to work alone, we can use the binomial probability formula. Since each worker has a probability \( p = 0.77 \) of driving to work alone, the probability that all 8 workers drive to work alone is given by:

\[
P(\text{all 8}) = p^n
\]

where \( p = 0.77 \) is the probability that a worker drives to work alone, and \( n = 8 \) is the number of workers.

Substituting the values:

\[
P(\text{all 8}) = (0.77)^8
\]

Now, we will calculate \( (0.77)^8 \):

\[
(0.77)^8 \approx 0.2631
\]

Now let's round to the nearest thousandths:

\[
P(\text{all 8}) \approx 0.263
\]

Thus, the probability that all 8 randomly chosen workers drive to work alone is approximately **0.263**.