According to a survey, 15 percent of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work? Round the answer to the nearest thousandth. cap p times k successes is equal to n cap c sub k p to the k th power open paren 1 minus p close paren raised to the n minus k power n cap c sub k is equal to the fraction with numerator n factorial and denominator open paren n minus k close paren factorial times k factorial
Use the binomial probability formula with n = 10, k = 6, and p = 0.15: C(10, 6)(0.15)^6(0.85)^4. This is approximately 0.001249, which rounds to 0.001 to the nearest thousandth. The correct choice is 0.001.
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