Let Xi = 1 denote Heads and Xi = 0 Tails in the ith toss. Consider 3 independent tosses X1, X2, X3 of a biased coin with

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Let Xi = 1 denote Heads and Xi = 0 Tails
in the ith toss. Consider 3 independent tosses
X1, X2, X3 of a biased coin with
the probability of a Head given by P(Xi = 1) = 6/10;
Calculate (fully justify your computations):
(a) P(X1 + X2 + X3 = 2)
(b) P(X1 + X2 + X3 = 2 |
X1 = 1)
(c) P(X1 + X2 = 2 | X3 = 0)
(d) P(X1 + X2 = 2 | X3 = 1)