Suppose we toss a coin once and let p be the probabilty of h

Suppose we toss a coin once and let p be the probabilty of heads. Let X denote the number of heads and let Y denote the number of tails.

(a) Prove that X and Y are dependent.

Solution

P(X=1) = 1/2 , P(X=0) = 1/2

P(Y=0) = 1/2 , P(Y=1) = 1/2

P(X=1|Y=0) = 1 ,

P(X=0|Y=1) = 1

hence X and Y are dependent