Probability

Question

two cards are selected at random(without replacement) from a well shuffled standard deck (52 cards with 4 ACES) of playing cards.  What is the probability that:

 

a.  They are both ACES?(show your work)

b.  Neither of them is an ACE? (show your work)

Answer 1

a.       ₄C₂/₅₂C₂=1/221  two aces out of four/choose 2 cards from deck

 

b.      ₄₈C₂/₅₂C₂=188/221  two cards not aces/choose 2 cards from deck

 

Answer 2

a.

First ace, 4/52, or 1/13

Second ace, 3/51

Both aces, (4/52)(3/51), or 12/2652, or 1/221

 

b.

First none ace, 48/52

Second none ace, 47/51

Both none aces, (48/52)(47/51), or 2256/2652, or 188/221