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Nov 2017 p63 q1
3020
A statistics student asks people to complete a survey. The probability that a randomly chosen person agrees to complete the survey is 0.2. Find the probability that at least one of the first three people asked agrees to complete the survey.
Solution
Let the probability that a person agrees to complete the survey be 0.2. Therefore, the probability that a person does not agree is 0.8.
The probability that none of the first three people agree to complete the survey is given by:
\((0.8)^3 = 0.512\)
Thus, the probability that at least one person agrees is:
\(1 - (0.8)^3 = 1 - 0.512 = 0.488\)
Alternatively, using the binomial probability formula, the probability that exactly one, two, or three people agree can be calculated and summed: