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      Question

      Two hats are picked at random, what is the probability

      that one is blue and one is yellow? A box contains 6 red, 4 blue, 2 green and 4 yellow hats.
      A 3/19 Correct Answer Incorrect Answer
      B 2/11 Correct Answer Incorrect Answer
      C 4/15 Correct Answer Incorrect Answer
      D 2/15 Correct Answer Incorrect Answer
      E None of these 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 = ¹⁶C_2 = (16 × 15 )/(2 × 1) = 120 Let E= event of drawing two hats so that one is blue and one is yellow. n(E) = ⁴C_1×⁴C_1 = 4 × 4 = 16 ∴ P (E) = (n(E))/(n(S)) = 16/120 = 2/15

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