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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NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper
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  1. 25/39 
  2. 14/27
  3. 10/21 
  4. 12/51

Answer (Detailed Solution Below)

Option 1 : 25/39 
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Given:

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.

Latest NIELIT Scientific Assistant Updates

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-> A total number of 113 revised vacancies have been announced for the post of Scientific Assistant in Computer Science (CS), Information Technology (IT), and Electronics & Communication (EC) streams.

-> Online application form, last date has been extended up to from 17th April 2025.

->The NIELT has revised the Essential Qualifications for the post of Scientific Assistant. Candidates must possess (M.Sc.)/ (MS)/ (MCA) / (B.E.)/ (B.Tech) in relevant disciplines.

 

-> The NIELIT Scientific Assistant 2025 Notification has been released by the National Institute of Electronics and Information Technology (NIELIT).

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