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Out of 13 applicants for a job there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is
- a)25/39
- b)14/39
- c)5/13
- d)10/13
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Probability of selecting at least one woman out of two persons for the job can be calculated by finding the probability of selecting two men and subtracting it from 1.
Probability of Selecting Two Men:
The probability of selecting a man from the 8 men applicants is 8/13. Since there are 8 men and we need to select 2 men, we can use the combination formula. The number of ways to select 2 men from a group of 8 men is given by:
C(8, 2) = 8! / (2!(8-2)!) = (8 * 7) / (2 * 1) = 28
Therefore, the probability of selecting two men is 28/13C2.
Probability of Selecting At Least One Woman:
To find the probability of selecting at least one woman, we subtract the probability of selecting two men from 1.
P(at least one woman) = 1 - P(two men)
P(two men) = 28/13C2
To calculate P(at least one woman), we can substitute the values in the formula:
P(at least one woman) = 1 - (28/13C2)
13C2 = 13! / (2!(13-2)!) = (13 * 12) / (2 * 1) = 78
Therefore, P(at least one woman) = 1 - (28/78) = 50/78 = 25/39.
Hence, the correct answer is option A) 25/39.
Probability of Selecting Two Men:
The probability of selecting a man from the 8 men applicants is 8/13. Since there are 8 men and we need to select 2 men, we can use the combination formula. The number of ways to select 2 men from a group of 8 men is given by:
C(8, 2) = 8! / (2!(8-2)!) = (8 * 7) / (2 * 1) = 28
Therefore, the probability of selecting two men is 28/13C2.
Probability of Selecting At Least One Woman:
To find the probability of selecting at least one woman, we subtract the probability of selecting two men from 1.
P(at least one woman) = 1 - P(two men)
P(two men) = 28/13C2
To calculate P(at least one woman), we can substitute the values in the formula:
P(at least one woman) = 1 - (28/13C2)
13C2 = 13! / (2!(13-2)!) = (13 * 12) / (2 * 1) = 78
Therefore, P(at least one woman) = 1 - (28/78) = 50/78 = 25/39.
Hence, the correct answer is option A) 25/39.
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