Three cards:
First card is a heart. There are 13 hearts in a normal deck:
[tex]P=\frac{13}{52}=\frac{1}{4}[/tex]Second card is a diamond: there are 13 diamonds:
[tex]P_2=\frac{13}{52}=\frac{1}{4}[/tex]Third: The card in not a spade, WITHOUT replacement.
There are 13*3 card that are not spade:
[tex]P_3=\frac{13*3}{52}=\frac{3}{4}[/tex]The probability will be given by:
[tex]PTotal=P\cap P_2\cap P_3[/tex]Replacing:
[tex]PTotal=\frac{1}{4}*\frac{1}{4}*\frac{3}{4}=\frac{3}{64}=0.0468\approx0.047[/tex]The answer is: 0.047.
