A box contains coupons labeled 1,2,3,....n. A coupon is picked at random and the number x is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is ([.] is greatest integer function, and the summations are from k = 1 to n)

A. 1/2
B. 1n2Σ[nk]
C. -1n + 1n2Σ[nk]
D. -1n + 2n2Σ[nk]

2 Answers

Sayan bisal ·


Shaswata Roy ·

You can choose x in n ways and y in n ways.

Let y>x,
Number of multiples of x within 1 to n is = \lfloor\frac{n}{x}\rfloor

Hence probability that x divides y = \frac{\lfloor\frac{n}{x}\rfloor}{n^2}

x ranges from 1 to n,

Therefore the required probability =


So I think the answer should be (B).

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