Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.) Required:
a. Find the probability that the first card is a face card and the second is NOT a face card.
b. Find the probability that they are both face cards.
c. Find the probability that the second is a face card given the first is NOT a face card.

The answer is below

Step-by-step explanation:

There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards

a. Find the probability that the first card is a face card and the second is NOT a face card.

There are 12 first card, the probability that the first card is a face card is 12/52.

Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:

The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card)  = 12/52 × 40/51 = 40/221

b) Find the probability that they are both face cards.

The probability that the first card is a face card is 12/52.

Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:

The probability that they are both face cards = P(first is face card) × P(second is face card)  = 12/52 × 11/51 = 11/221

c) Find the probability that the second is a face card given the first is NOT a face card.

The probability that the first card is not a face card = 40/52

Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:

The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card)  = 40/52 × 12/51 = 40/221