XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

XAT Previous Year Paper | XAT QADI Questions | Question 28

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Question 28 : I have five 10-rupee notes, three 20-rupee notes and two 50-rupee notes in my wallet.

If three notes were taken out randomly and simultaneously, what is the probability that at least 90 rupees were taken out?

  1. 1/15
  2. 7/60
  3. 3/20
  4. 11/60
  5. 1/20

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Explanatory Answer

Given that there are five 10-rupee notes, three 20-rupee notes, and two 50-rupee notes.
To get at least 90 rupees within three notes, you should have at least one 50-rupee note.
Let us consider taking only one 50-rupee note and the remaining two from other denominations
If we take one 50-rupee note and two 10-rupee notes do not add up to 90.
From this, we get that the remaining notes should be 20-rupee notes, So that we get 2C1 × 3C2 = 2 × 3 = 6
Now, Let us consider taking two 50-rupee notes and the remaining one from other denominations.
Two 50-rupee notes are added up to 100, so, we can take any note from the remaining.
So we get 2C2 × 5C1 + 2C2 × 3C1 = 5 + 3 = 8
Total chances of taking 3 notes is 10C3 = 120
The probability of getting at least 90 rupees = \(\frac{6+8}{120}\) = \(\frac{14}{120}\) = \(\frac{7}{60}\)
The correct answer is \(\frac{7}{60}\)

The answer is '7/60'

Choice B is the correct answer.

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