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.
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