Among 27-to 32-year-olds, 27% say they have operated heavy machinery while under

Question

Among 27-to 32-year-olds, 27% say they have operated heavy machinery while under the influence of sugar. Suppose three 27-to 32-year-olds are selected at random. (a) What is the probability that at least one has not operated heavy machinery while under the influence of sugar? (b) What is the probability that at least one has operated heavy machinery while under the influence of sugar? (a) The probability that at least one has not operated heavy machinery while under the influence of sugar is Round to four decimal places as needed.) (b) The probability that at least one of the three randomly selected adults has operated heavy machinery while under the influence of sugar is Round to four decimal places as needed.)

Explanation / Answer

P(operated) = 0.27

P(not operated) = 1 - 0.27 = 0.73

n = 3

a) P(at least one not operated) = 1 - P(zero not operated)

                                                  = 1 - 3C0 * 0.730 * 0.273

                                                  = 1 - 0.0197

                                                  = 0.9803

b) P(at least one operated) = 1 - P(zero operated)

                                            = 1 - 3C0 * 0.270 * 0.733

                                            = 1 - 0.3890

                                            = 0.6110

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