GATE ME 2020 Set 1 — Question 33
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General Aptitude → Quantitative Aptitude → Elementary Statistics & Probability
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Question
A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is ______ (round off to 2 decimal places).
Correct answer
0.9 to 0.95
Solution
Total number of candidates = .
Number of vacancies to be filled = 4.Total number of ways to choose 4 candidates from 8 is:Let be the event that at least one woman is selected. It is easier to calculate the probability of the complement event , where no women are selected (i.e., all 4 selected are men).
Number of ways to choose 4 men from 5 is:The probability of selecting no women is:The probability of selecting at least one woman is:Rounding off to 2 decimal places, we get .
Number of vacancies to be filled = 4.Total number of ways to choose 4 candidates from 8 is:Let be the event that at least one woman is selected. It is easier to calculate the probability of the complement event , where no women are selected (i.e., all 4 selected are men).
Number of ways to choose 4 men from 5 is:The probability of selecting no women is:The probability of selecting at least one woman is:Rounding off to 2 decimal places, we get .
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