Question

find the probability of drawing a spade or a face card from a standard deck of cards

Answer 1

You want to know the probability of getting one of these 22 cards
                                                       J♥ Q♥ K♥
                                                       J♦ Q♦ K♦
 A♠ 2♠ 3♠ 4♠ 5♠ 6♠ 7♠ 8♠ 9♠ 10♠ J♠ Q♠ K♠
                                                       J♣ Q♣ K♣
 out of these 52 cards:
A♥2♥3♥4♥5♥6♥7♥8♥9♥10♥J♥Q♥K♥
A♦2♦3♦4♦5♦6♦7♦ 8♦9♦10♦J♦Q♦ K♦
A♠2♠3♠ 4♠ 5♠6♠7♠ 8♠ 9♠10♠J♠Q♠K♠
A♣2♣3♣4♣5♣6♣7♣8♣9♣10♣J♣Q♣K♣

That's 22 out of 52, which we make into a fraction which reduces to 22/52 which reduces it to 11/26

Answer 2

Answer:

There are of course 52 cards in the standard deck. A face card is a jack, queen or king, and each comes in four suits, so 12 face cards.  

Four 3s mean 16 cards of 52 satisfy our event.

p = \dfrac{16}{52} = \dfrac{4}{13}

Step-by-step explanation: