 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/16/b/i/solution

Let

Y

indicate whether the draw from the second bag is green. It is independent of

X

, with

P (Y = 1) = 1/3

and

P (Y = 0) = 2/3

. Exactly one green overall arises from the disjoint alternatives

(X, Y) = (1, 0)

(0, 1)

. Therefore

P (X + Y = 1) = \frac{3}{5} \frac{2}{3} + \frac{1}{10} \frac{1}{3} = \frac{13}{30} .

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