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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Probability

NDA 2022 · Mathematics · Probability

There are 90 applicants for a job. Some of them are graduates. Some...

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		189
Less than 3 years
experience		3627
Let GG be the event that the first applicant interviewed is a graduate and TT be the event that first applicant interviewed has at least 3 years experience. What is P(Tˉ∣Gˉ)P(\bar{T} \mid \bar{G}) equal to?

Options

  1. A14\frac{1}{4}
  2. B13\frac{1}{3}
  3. C35\frac{3}{5}
  4. D34\frac{3}{4}

Correct answer

D. 34\frac{3}{4}

Step-by-step solution

∵n(T‾∩G‾)=27n(G‾)=9+27=36∴P(T‾/G‾)=P(T‾∩G‾)P(G‾)\begin{aligned} & \because \mathrm{n}(\overline{\mathrm{T}} \cap \overline{\mathrm{G}})=27 \\ & \mathrm{n}(\overline{\mathrm{G}})=9+27=36 \\ & \therefore \mathrm{P}(\overline{\mathrm{T}} / \overline{\mathrm{G}})=\frac{\mathrm{P}(\overline{\mathrm{T}} \cap \overline{\mathrm{G}})}{\mathrm{P}(\overline{\mathrm{G}})}\end{aligned}\frac{\frac{27}{90}}{\frac{36}{90}}=\frac{27}{36}=\frac{3}{4}$
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