7 Deck of Cards Suppose you are dealt two cards from a standard deck of playing

Question

7 Deck of Cards Suppose you are dealt two cards from a standard deck of playing cards. There are 4 different suits (clubs, diamonds, hearts, spades) and 13 different denominations (Ace, 2, 3, 10, Jack, Queen, King) a) What is the probability of being dealt a pair of aces? (This means that both the cards are aces) b) There are 13 pairs possible (Aces through Kings). What is the probability of being dealt a pair of any type (that is, the probability of being dealt a pair of aces OR 2s OR 3s, etc...).?

Explanation / Answer

a)P(dealt a pair of aces)=P(first card is ace)*P(second ace|first ace)=(4/52)*(3/51)=1/221

b)

as there are 13 pairs ; therefore probability of being dealt a pair of any type

=P(selecting any card from 52)*P(second card from rest of 3 of that rank)

=(52/52)*(3/51)=1/17

c)

P(two cards of same suit)=P(first can be any card from 52)*P(second should be rest of 12 of same suit)

=(52/52)*(12/51)=4/17

d)

as there are total 16 cards greater than a 10

hence P(two cards greater than a 10)=(16/52)*(15/51)=20/221

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