Among 44- to 49-year-olds, 27% say they have written an editorial letter while u

Question

Among 44- to 49-year-olds, 27% say they have written an editorial letter while under the influence of peer pressure. Suppose six 44- to 49-year-olds are selected at random. What is the probability that at least one has not written an editorial letter while under the influence of peer pressure? (b) What is the probability that at least one has written an editorial letter while under the influence of peer pressure? The probability that at least one has not written an editorial letter while under the influence of peer pressure is. (Round to four decimal places as needed.) The probability that at least one of the six randomly selected adults has written an editorial letter while under the influence of peer pressure is. (Round to four decimal places as needed.)

Explanation / Answer

This is a Bernoulli's process with parameter p = 0.27

(a)

P(atleast 1 hasn't written letter under pressure) = 1-P(all have written under pressure)

P(all have written under pressure) = 6C6 * 0.276 * (1-0.27)0 = 0.000387

So,

P(atleast 1 hasn't written letter under pressure) = 1 - 0.000387 = 0.999613

(b)

P(atleast 1 has written letter under pressure) = 1-P(all have written without pressure)

P(all have written without pressure) = 6C6 * 0.270 * (1-0.27)6 = 0.151

So,

P(atleast 1 has written letter under pressure) = 1 - 0.151 = 0.849

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