Answer to Question #154686 in Statistics and Probability for Shawnitra Jackson

Question

The workers union at a particular university is quite strong. About 94% of all workers employed by the University belong to the workers union. Recently, the workers went on strike, and now a local TV station plans to interview 5 workers (chosen at random) at the University to get their opinions on the street. What is the probability that exactly 4 of the workers interview our union members? Round your response to at least three decimal places.

Answer 1

The probability that one random worker belongs to the workers union (WU) is equal to 0.94, and the probability that the worker does not belong to WU is equal to 0.06.

The probability that only the first (only the second, etc, only the 5th) worker does not belong to WU is equal to 0.06*0.94⁴= 0.046845

The probability that exactly 4 workers interviewed belong to WU is the sum of the probabilities that only the first worker does not belong to WU, only the second onedoes not belong to WU, etc, and equals to 5 * 0.046845 = 0.234225.

Answer. 0.234 (= 23.4%)