ANSWER
P(jack or spade) = 4/13
EXPLANATION
There are 4 jacks in a deck of 52 cards, one for each suit, so the probability of drawing a jack is,
[tex]P(jack)=\frac{4}{52}[/tex]Each suit has 13 cards, so there are 13 spades in the 52-card deck. The probability of drawing a spade is,
[tex]P(spade)=\frac{13}{52}[/tex]There is only one jack of spades, so the probability of drawing that particular card is,
[tex]P(jack.of.spades)=\frac{1}{52}[/tex]The probability of drawing a jack or a spade is the probability of the union of the events where a jack is drawn or a spade is drawn,
[tex]P(jack.or.spade)=P(jack\cup spade)[/tex]And this is, by definition,
[tex]P(jack\cup spade)=P(jack)+P(spade)-P(jack\cap spade)[/tex]The probability of the intersection of the events is the probability that the card drawn is a jack of spades,
[tex]P(jack\cup spade)=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{4+13-1}{52}=\frac{16}{52}=\frac{4}{13}[/tex]Hence, P(jack or spade) = 4/13.
