Suppoe a simple consist of the integers 1,2,….2n, the probability of choosing an integer k is proportion to log k . Show that the conditional probability of choosing the integer 2, given that even integer is chosen is `(log2)/((n) log 2 +log(n!))` .

Let S = {1, 2, … 100}. The probability of choosing an integer k, 1lekle100 is proportional to log k. The conditional probability of choosing the integer 2, given that an even integer is chosen is

Show that n^2-1 is divisible by 8, if n is an odd positive integer.

If the probability of choosing an integer 'k' out of 2n integers 1, 2, 3, …, 2n is inversely proportional to k^4(1lekle2n) . If alpha is the probability that chosen number is odd and beta is the probability that chosen number is even, then (A) alpha gt 1/2 (B) alpha gt 2/3 (C) beta lt 1/2 (D) beta lt 2/3

Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.

Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.

If n is a positive integer then int_(0)^(1)(ln x)^(n)dx is :

If the probability of chossing an interger "k" out of 2m integers 1,2,3,….,2m is inversely proportional to k^(4)(1leklem).Ifx_(1) is the probability that chosen number is odd and x^(2) is the probability that chosen number is even, then

Using contrapositive method prove that, if n^(2) is an even integer , then n is also an even integer.

Using contrapositive method prove that , if n^(2) is an even integer, then n is also an even integer.

The greatest integer less than or equal to the number log_2(15)xx log_(1/6)2xx log_3(1/6) is