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16 Sep 2014, 00:23
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Out of the 10 applicants interviewed for a position, which includes Paul and Jen, what is the probability that neither Paul nor Jen is selected for the first interview?
A. \(\frac{1}{10}\)
B. \(\frac{1}{9}\)
C. \(\frac{1}{2}\)
D. \(\frac{4}{5}\)
E. \(\frac{9}{10}\)
A. \(\frac{1}{10}\)
B. \(\frac{1}{9}\)
C. \(\frac{1}{2}\)
D. \(\frac{4}{5}\)
E. \(\frac{9}{10}\)
16 Sep 2014, 00:23
Kudos
Bookmarks
Official Solution:
Out of the 10 applicants interviewed for a position, which includes Paul and Jen, what is the probability that neither Paul nor Jen is selected for the first interview?
A. \(\frac{1}{10}\)
B. \(\frac{1}{9}\)
C. \(\frac{1}{2}\)
D. \(\frac{4}{5}\)
E. \(\frac{9}{10}\)
There are 10 applicants and 2 of them are Paul and Jen.
If neither Paul nor Jen is selected for the first interview, then the first interviewee can be one of the remaining 8 applicants.
So, the probability is \(\frac{8}{10}\), which is \(\frac{4}{5}\).
Answer: D
Out of the 10 applicants interviewed for a position, which includes Paul and Jen, what is the probability that neither Paul nor Jen is selected for the first interview?
A. \(\frac{1}{10}\)
B. \(\frac{1}{9}\)
C. \(\frac{1}{2}\)
D. \(\frac{4}{5}\)
E. \(\frac{9}{10}\)
There are 10 applicants and 2 of them are Paul and Jen.
If neither Paul nor Jen is selected for the first interview, then the first interviewee can be one of the remaining 8 applicants.
So, the probability is \(\frac{8}{10}\), which is \(\frac{4}{5}\).
Answer: D
07 Jul 2021, 21:48
Kudos
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Probability of any one of the 10 persons being invited for the first interview = \(\frac{1}{10}\)
Probability(Neither Paul nor Jen are at the first interview) = 1 – Probability(Either Paul or Jen are at the first interview)
Probability of either Paul or Jen being invited first = \(\frac{1}{10} + \frac{1}{10}\) = \(\frac{2}{10}\).
Note that if Paul is invited, Jen is not and vice versa and that is why we just have to add \(\frac{1}{10}\) with \(\frac{1}{10}\).
Therefore, probability that neither Paul nor Jen are at the first interview = 1 – \(\frac{2}{10}\) = \(\frac{8 }{ 10}\) = \(\frac{4}{5}\).
The correct answer option is D.
Hope that helps!
Aravind BT
Probability(Neither Paul nor Jen are at the first interview) = 1 – Probability(Either Paul or Jen are at the first interview)
Probability of either Paul or Jen being invited first = \(\frac{1}{10} + \frac{1}{10}\) = \(\frac{2}{10}\).
Note that if Paul is invited, Jen is not and vice versa and that is why we just have to add \(\frac{1}{10}\) with \(\frac{1}{10}\).
Therefore, probability that neither Paul nor Jen are at the first interview = 1 – \(\frac{2}{10}\) = \(\frac{8 }{ 10}\) = \(\frac{4}{5}\).
The correct answer option is D.
Hope that helps!
Aravind BT
