Question

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

Answer 1

$P(H=0)=\frac{3}{4}*\frac{3}{4}=\frac{9}{16}.$

$P(H=1)=\frac{1}{4}*\frac{3}{4}+\frac{3}{4}*\frac{1}{4}=\frac{6}{16}=\frac{3}{8}.$

$P(H=2)=\frac{1}{4}*\frac{1}{4}=\frac{1}{16}.$