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      Question

      Two hats are picked at random, what is the probability

      that all hats are of green colour? A box contains 6 red, 4 blue, 2 green and 4 yellow hats.
      A 1/150 Correct Answer Incorrect Answer
      B 22/145 Correct Answer Incorrect Answer
      C 9/115 Correct Answer Incorrect Answer
      D 3/116 Correct Answer Incorrect Answer
      E 1/120 Correct Answer Incorrect Answer

      Solution

      Total number of hats = 6 + 4 + 2 + 4 = 16 Let S be the sample space. Then, n(S) = number of ways of drawing 2 hats out of 16 = ¹βΆC_β‚‚ = (16 × 15)/( 2 × 1) = 120 Let E= event of drawing all the hats are of green colour n(E) = ²C_β‚‚ = 1 ∴ P (E) = (n(E))/(n(S)) = 1/120

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