Question
Download Solution PDFOut of 13 applicants for a job there are 5 women and 8 men. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a women.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total applicants = 13 (5 women + 8 men)
2 persons are to be selected
Required: Probability that at least one selected is a woman
Formula used:
At least one woman = 1 − Probability of selecting **only men**
Calculations:
Total ways to choose 2 from 13 = 13C2 = (13×12)/2 = 78
Ways to choose 2 men from 8 = 8C2 = (8×7)/2 = 28
⇒ Probability of only men = 28 / 78
⇒ Probability of at least one woman = 1 − 28/78 = 50/78 = 25/39
∴ The required probability is 25/39.
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