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UPSC NDA I 2022 Mathematics Solved Paper

Question Numbers: 112-114

Consider the following data for the next three (03) items that follow :

There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience.

	Number of graduates	Number of non-graduates
At least 3 years experience	18	9
Less than 3 years experience	36	27

Let G be the event that the first applicant interviewed is a graduate and T be the event that first applicant interviewed has at least 3 years experience.

Question : 114 of 120

Marks: +1, -0

What is

P(\overline{T} \mid \overline{G})

equal to?

$\frac{1}{4}$
$\frac{1}{3}$
$\frac{3}{5}$
$\frac{3}{4}$

Validate

Solution:

Concept:

Conditional probability:

P(A|B) = \frac{P(A \cap B)}{P(B)}

Here

A = \overline{T}

(less than 3 years experience) and

B = \overline{G}

(not a graduate).

Explanation:

From the table: number of applicants who are not graduates,

n(\overline{G}) = 27 + 9 = 36

Number who are not graduates and have less than 3 years experience,

n(\overline{T} \cap \overline{G}) = 27

Thus,

P(\overline{T} \mid \overline{G}) = \frac{n(\overline{T} \cap \overline{G})}{n(\overline{G})} = \frac{27}{36} = \frac{3}{4}

Answer:

\frac{3}{4}

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