Three cards are dealt from a standard well shuffled deck The

Three cards are dealt from a standard, well shuffled deck. The first two cards are flipped over, revealing the Ace of Spades as the first card and the 8 of clubs as the second card. Given this information, find the probability that the third card is an ace in two ways: using the definition of conditional probability, and by symmetry.

Solution

a) Using the definition of conditional probability:
Let A : Third card is ace
B: First card is ace of spades
C: Second card is 8 of clubs
P(A/(B and C)) = P(A and B and C) / P(B and C)
=(1/52*1/51*3/50)/(1/52*1/51)
= 3/50
= 0.06 Answer   

b)By Symmetry:
First card is ace of spades and second is 8 of club.
Therefore, 3 Aces are still left in (52-2)-50 cards.
Therefore, Probability ( Third card is Ace) = 3/50 = 0.06 Answer