Out 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.

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Question

This question was previously asked in

NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper

Answer 1

Given:

Number of women (W) = 5

Number of men (M) = 8

Total applicants = 13

Number of persons to be selected = 2

Formula used:

Probability of at least one woman = 1 - Probability of selecting no woman

Calculation:

Total ways to select 2 persons from 13 = ¹³C₂

⇒ 13C2 \( = \frac{13 \times 12}{2 \times 1} = 78 \)

Ways to select 2 men from 8 = ⁸C2

⇒ 8C2 \(= \frac{8 \times 7}{2 \times 1} = 28\)

Probability of selecting no woman = 8C2 / 13C2 \( = \frac{28}{78} = \frac{14}{39}\)

Probability of selecting at least one woman = 1 - Probability of selecting no woman

⇒ \( 1 - \frac{14}{39} = \frac{39 - 14}{39} = \frac{25}{39}\)

∴ The correct answer is option (1).

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