a deck has four cards - an ace of spades, an ace of hearts, an ace of diamonds and an ace of club. two cards will be drawn with replacement. let H denote the number of the ace of hearts is drawn
P(H=0)=34∗34=916.P(H=0)=\frac{3}{4}*\frac{3}{4}=\frac{9}{16}.P(H=0)=43∗43=169.
P(H=1)=14∗34+34∗14=616=38.P(H=1)=\frac{1}{4}*\frac{3}{4}+\frac{3}{4}*\frac{1}{4}=\frac{6}{16}=\frac{3}{8}.P(H=1)=41∗43+43∗41=166=83.
P(H=2)=14∗14=116.P(H=2)=\frac{1}{4}*\frac{1}{4}=\frac{1}{16}.P(H=2)=41∗41=161.
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