Answer:
Step-by-step explanation:
It can be clearly observed that [tex]X\in{0,1,2}[/tex] and [tex]Y\in {0,1}[/tex]
Now lets find the probabilities of all possible combinations
[tex]P(X=0, Y=0)=P(Y=0|X=0)P(X=0)=0[/tex]
Since it is impossible that the coin ha flipped in different ways given that all the time the tail has fallen
[tex]P(X=1,Y=0)=P(Y=0|X=1)P(X=1)=1\times2\times(\frac{1}{2} )^2[/tex] =1/2
[tex]P(X=2,Y=0)=P(Y=0|X=2)P(X=2)=1\times2\times(\frac{1}{2} )^2[/tex] =1/2
and similarly,
[tex]P(X=0,Y=1)=P(Y=1|X=0)P(X=0)=1\times(\frac{1}{2} )^2= 1/4[/tex]
[tex]P(X=1,Y=1)=P(Y=1|X=1)P(X=1)=0[/tex]
[tex]P(X=2,Y=1)=P(Y=1|X=2)P(X=2)=1\times(\frac{1}{2} )^2=1/4[/tex]
