GATE 2018 MA Probability

Question

Answer 1

Let, p=1/2... {For easiness f our calculations...!!}
So, For P(x1=2) = 1/4 = P(x2=2)
P(x1=2).P(x2=2) = 1/4 x 1/4 = 1/16

P(x1 + x2 = 4) = (1/2)*(1/2)^2 + (1/2)^2*(1/2) + (1/2)*(1/2) = 1/8 + 1/16 = 3/16

Hence, we need to find P(x1=2 given x1+x2=4) = P(x1=2) * P(x2=2) / P(x1+x2=4)
                                                                            =  (1/4 * 1/4) / 3/16
                                                                            = 1/16 * 16/3 = 1/3 = 0.333