A deck of cards has the 7 of hearts missing A card is dealt

A deck of cards has the 7 of hearts missing. A card is dealt from this (partial) deck. Let A = event that this card is an Ace. Let C = event that this card is a club. Is the probability (A|C) > probability (A)? Or is probability (A|C) < probability (A)

Solution

P(A) = 1/4

P(C) = 13/51

P ( A| C) = P( the card drawn is an ace of club)/ P( the card is a club)

= (1/13) /(13/51) = 1/51

Therefore, P(A|C) < P(A)