Spades is a card game played with a regular deck of cards dealt out completely (

Question

Spades is a card game played with a regular deck of cards dealt out completely (13 cards each) to 4 players each hand. You play with a partner who sits across from you, but you do not know what cards they have. In the game, spades are trump cards, which means they win over other suits, and in general it is desirable to have as many as possible each hand.

What is the probability you have all 4 Aces in your hand?

What is the probability you have the Ace of spades, King of spades, Queen of spades, and Jack of spades in your hand?

What is the probability you have at least 4 spades in your hand?

Given that you have at least 4 spades in your hand, what is the probability you and your partner have at least 8 spades between the two of you?

Given that you have at least 4 spades in your hand, what is the probability your partner has zero in their hand?

Explanation / Answer

(a)

Probability of having all the aces in your hand = (48C9/52C13) = 0.00264

(b)

Probability of having the ace of spades, King of spades, Queen of spades, and Jack of spades in your hand = (48C9/52C13) = 0.00264

(c)

Probability you have at least 4 spades in your hand = 1 - Probability you have less than 4 spades in your hand

Now,

Probability you have less than 4 spades in your hand = (39C13/52C13) + ((39C12*13C1)/52C13) + ((39C11*13C2)/52C13) + ((39C10*13C3)/52C13) = 0.585

So,

Probability you have at least 4 spades in your hand = 1 - 0.585 = 0.415

Hope this helps !

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