XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

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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?

Video Explanation

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.