Given:
The total cards is: 52
Number of spade cards: 13
Number of red cards: 26
Number of face cards: 12
Therefore,
[tex]P(\text{spade)}=\frac{13}{52}=\frac{1}{4}[/tex][tex]P(red)=\frac{26}{52}=\frac{1}{2}[/tex][tex]P(\text{face)}=\frac{12}{52}=\frac{3}{13}[/tex]The probability that the first card will be a spade, the second card will be a red card, and the third card will be a face card is given by:
[tex]P(spade\text{ and red and face)=P(spade)}\cdot P(red)\cdot P(face)[/tex]Substitute:
[tex]=\frac{1}{4}\cdot\frac{1}{2}\cdot\frac{3}{13}=\frac{1\cdot1\cdot3}{4\cdot2\cdot13}=\frac{3}{104}[/tex]Answer: 3/104
