Two hats are picked at random, what is the probability that one is blue and one is yellow?
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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