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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. The probabilty that atleast one of selected persons will be a Woman is?
- a)77/91
- b)54/91
- c)45/91
- d)40/91
- e)None of these
Correct answer is option 'A'. 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 atleast one woman = 1 – 14/91 = 77/91
Probability of selecting no woman = 14/91
Probability of selecting atleast one woman = 1 – 14/91 = 77/91
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
Out of 14 applicants for a job, there are 6 women and 8 men. It is des...
Given information:
Total number of applicants = 14
Number of women applicants = 6
Number of men applicants = 8
Number of persons to be selected = 2
Probability that atleast one of selected persons will be a Woman is to be found.
Solution:
Total number of ways to select 2 persons out of 14 applicants = 14C2 = (14*13)/(2*1) = 91
Let A be the event of selecting atleast one woman and B be the event of selecting only men.
P(A) = 1 - P(B) (since either A or B will happen)
Probability of selecting only men = Number of ways to select 2 men out of 8 men applicants / Total number of ways to select 2 persons
= 8C2 / 14C2
= (8*7)/(2*1) / (14*13)/(2*1)
= 28/91
Therefore, P(A) = 1 - 28/91
= 63/91
= 77/91
Hence, the probability that atleast one of selected persons will be a Woman is 77/91.
Answer: Option A (77/91)
Total number of applicants = 14
Number of women applicants = 6
Number of men applicants = 8
Number of persons to be selected = 2
Probability that atleast one of selected persons will be a Woman is to be found.
Solution:
Total number of ways to select 2 persons out of 14 applicants = 14C2 = (14*13)/(2*1) = 91
Let A be the event of selecting atleast one woman and B be the event of selecting only men.
P(A) = 1 - P(B) (since either A or B will happen)
Probability of selecting only men = Number of ways to select 2 men out of 8 men applicants / Total number of ways to select 2 persons
= 8C2 / 14C2
= (8*7)/(2*1) / (14*13)/(2*1)
= 28/91
Therefore, P(A) = 1 - 28/91
= 63/91
= 77/91
Hence, the probability that atleast one of selected persons will be a Woman is 77/91.
Answer: Option A (77/91)
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