Question

What is the probability of a face card given that the card is black?

Answer 1

The probability of a face card given that the card is black = 3/26

Explanation:

Points to remember

There are total 52 cards. It is divided into 4 suites, 13 each.

Spades, Clubs, Hearts and Diamonds

Spades and Clubs are black.

Hearts and Diamonds are red

In each suites there are 3 face cards.

To find the probability

There are total 52 cards. And 6 black face cards

The probability of a face card given that the card is black =6/52

= 3/26

Answer 2

P(face | Black) = 3/13

Explanation:

total number of cards in standard deck of cards = 52

Total number of face cards = 12

Then P(face cards) = 12/52

Total number of black cards = 26

Then P(black cards) = 26/52

Total number of cards that are both black and face cards = 6

Then P(black and face cards) = 6/52

Then conditional probability of getting face card given that the card is black is given by:

P(face | Black) = P( face & Black) / P(Black)

P(face | Black) = (6/52) / (26/52)

P(face | Black) = 6/26

P(face | Black) = 3/13