Question

Two cards are drawn at random from a deck of 52 cards without replacement. What is the probability of drawing a 2 and an Ace in that order?
A) 4/51
B) 1/13
C) 4/256
D) 4/663

Answer 1

Question: Two cards are drawn at random from a deck of 52 cards without replacement. What is the probability of drawing a 2 and an Ace in that order?

Solution: A deck of 52 cards has 4 suits of 13 each: "clubs ♣, diamonds. , hearts ♥ and spades ♠".

The 13 cards are: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king.

Probability of drawing a 2 = 4/52.

Probability of drawing an Ace = 4/51. (because there is no replacement so total card count reduced to 51).

Probability of drawing a 2 and an Ace = 4/52 * 4/51 = 4/663 i.e. Option D.

Answer 2

Number of cards in a deck = 52

Number of cards with "2" = 4

Number of cards with Ace = 4

Find the probability of getting a "2" on the first card and an "ace" on the second card (without replacement):

P(first a 2, then an ace) = (4/52)(4/51) = 4/663

Answer: (D) 4/663