GATE 2020 ME (ME1) – Question 33
A company fills four managerial vacancies from five men and three women. Every candidate is equally likely to be selected. Find the probability that at least one woman is selected, to two decimals.
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Correct answer: .90 to .95
Explanation
Use the complement: all four are men in $\binom54=5$ selections, out of $\binom84=70$. Hence $P=1-5/70=13/14=\mathbf{0.93}$ after rounding. Selection is without replacement.