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Out of 14 applicants for a job, there are 6 women and 8 men. It is desired to select 2 persons for the job.
Quantity I: Probability of selecting no woman
Quantity II: Probability of selecting at least one woman
  • a)
    Quantity I > Quantity II
  • b)
    Quantity I < Quantity II
  • c)
    Quantity I ≥ Quantity II
  • d)
    Quantity I ≤ Quantity II
  • e)
    Quantity I = Quantity II or relation cannot be established
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Out of 14 applicants for a job, there are 6 women and 8 men. It is des...
Man only = 8C2 = 14
Probability of selecting no woman = 14/91
Probability of selecting at least one woman = 1 – 14/91 = 77/91
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Most Upvoted Answer
Out of 14 applicants for a job, there are 6 women and 8 men. It is des...
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b)Quantity I > Quantity II
c)Quantity I = Quantity II
d)Cannot be determined from the given information

To find the probability of selecting no woman, we need to find the probability of selecting 2 men from the 8 men available. This can be calculated using combinations:

Number of ways to select 2 men out of 8 men = 8C2 = (8*7)/(2*1) = 28

Total number of ways to select any 2 persons out of 14 applicants = 14C2 = (14*13)/(2*1) = 91

Probability of selecting no woman = 28/91

To find the probability of selecting at least one woman, we can find the probability of selecting 2 persons and subtract the probability of selecting no woman:

Probability of selecting at least one woman = 1 - (28/91) = 63/91

Comparing the two quantities:

Quantity I: Probability of selecting no woman = 28/91
Quantity II: Probability of selecting at least one woman = 63/91

Since Quantity II is greater than Quantity I, the answer is (a) Quantity I < quantity="" ii.="" quantity="" />
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Out of 14 applicants for a job, there are 6 women and 8 men. It is desired to select 2 persons for the job.Quantity I: Probability of selecting no womanQuantity II: Probability of selecting at least one womana)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'B'. Can you explain this answer?
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