There are 4 women and 4 men sitting in a waiting room for job interview. If two of the applicants are selected at random, what is the probalility that both will

There are 4 women and 4 men sitting in a waiting room for job interview. If two of the applicants are selected at random, what is the probalility that both will be women?

There are 4 women and 4 men sitting in a waiting room for job interview. If two of the applicants are selected at random, what is the probalility that both will be women? ?

Created: 1 year ago | Updated: 1 week ago | Created By:

Md Kamal Uddin

1/2

3/7

3/4

3/14

0 11

Institution: EXIM BANK LTD Exam: Exim Bank Ltd - Trainee Officer - 29.05.2015 ||
Topic: Mathematics (সাধারণ গণিত) Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To find the probability that both selected applicants will be women, we first need to find the total number of ways to select 2 applicants out of 8 (4 women and 4 men). This can be calculated using combinations:

$Total number of ways to select 2 applicants out of 8 = (\binom{8}{2})$

$(\binom{�}{�}) = \frac{�!}{�! (� - �)!}$

$(\binom{8}{2}) = \frac{8!}{2! (8 - 2)!} = \frac{8!}{2! 6!} = \frac{8 \times 7}{2 \times 1} = 28$

Next, we need to find the number of ways to select 2 women out of 4:

$Number of ways to select 2 women out of 4 = (\binom{4}{2})$

$(\binom{4}{2}) = \frac{4!}{2! (4 - 2)!} = \frac{4!}{2! 2!} = \frac{4 \times 3}{2 \times 1} = 6$

Finally, we calculate the probability that both selected applicants will be women by dividing the number of ways to select 2 women by the total number of ways to select 2 applicants:

$Probability = \frac{Number of ways to select 2 women}{Total number of ways to select 2 applicants}$

$Probability = \frac{6}{28} = \frac{3}{14}$

So, the probability that both selected applicants will be women is $\frac{3}{14}$ . Therefore, the correct option is $\frac{3}{14}$ .

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There are 4 women and 4 men sitting in a waiting room for job interview. If two of the applicants are selected at random, what is the probalility that both will be women? ?

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