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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(G∣Tˉ)P(G \mid \bar{T}) equal to?

Options

  1. A27\frac{2}{7}
  2. B37\frac{3}{7}
  3. C47\frac{4}{7}
  4. D57\frac{5}{7}

Correct answer

C. 47\frac{4}{7}

Step-by-step solution

∵P(G∩T‾)=25P(Tˉ)=6390=710∴P(G/T‾)=P(G∩T‾)P(T‾)=25710=47\because \mathrm{P}(\mathrm{G} \cap \overline{\mathrm{T}})=\frac{2}{5}P(\bar{T})=\frac{63}{90}=\frac{7}{10}\therefore \mathrm{P}(\mathrm{G} / \overline{\mathrm{T}})=\frac{\mathrm{P}(\mathrm{G} \cap \overline{\mathrm{T}})}{\mathrm{P}(\overline{\mathrm{T}})}=\frac{\frac{2}{5}}{\frac{7}{10}}=\frac{4}{7}
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