Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.

Question: Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.

Solution:
The events of selection of two person is redefined as first is a girl and second is a boy or first is boy and second is a girl or first is a girl and second is a girl.
So the required probability = {(8/17) × (9/16)} + {(9/17) × (8/16)} + {(8/17) × (7/16)}
= (9/34) + (9/34) + (7/34)
= (9 + 9 + 7)/34
= 25/34