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COMEDK2023Morning ShiftMathematicsProbabilityActual

If a number n is chosen at random from the set 11,12,13, , 30 . Then, the probability that n is neither divisible by 3 nor divisible by 5, is

Options

  1. A13 20
  2. B9 20
  3. C7 20
  4. D11 20

Correct answer

D. 11 20

Step-by-step solution

The set of numbers is S = 11, 12, 13, , 30 . The total number of elements in S is 30 - 11 + 1 = 20 . Let A be the set of numbers in S divisible by 3. These are 12, 15, 18, 21, 24, 27, 30 . The number of elements in A is n(A) = 7 . Let B be the set of numbers in S divisible by 5. These are 15, 20, 25, 30 . The number of elements in B is n(B) = 4 . The set of numbers divisible by both 3 and 5 (i.e., divisible by 15) is A B = 15, 30 . The number of elements in A B is n(A B) = 2 . The number of elements divisible by 3

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