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A number n is chosen at random from s = 1, 2, 3, , 50 . Let A = n s : n is a prime , B = n s : n is a square and C = n s : n is a cube . Then, correct order of their probabilities is

Options

  1. Ap( ~B ) < p( ~A ) < p(C)
  2. Bp(A) > p(B) > p(C)
  3. Cp(A) > p(c) > p(B)
  4. Dp(A) < p(B) < p(C)

Correct answer

B. p(A) > p(B) > p(C)

Step-by-step solution

Primes up to 50: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 (A) = 15 , p(A) = 15 50 Perfect squares up to 50: 1,4,9,16,25,36,49 (B) = 7 , p(B) = 7 50 Perfect cubes up to 50: 1,8,27 (C) = 3 , p(C) = 3 50 Since 15 > 7 > 3 : p(A) > p(B) > p(C)

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