A card is drawn from a standard deck of 52 cards, what is the probability that it is a black

The "hard way":

To get a black card on the second draw you must get either "red, black" or "black, black".

1) "red, black": There are 52 cards in the deck, 26 or them red. The probability the first card drawn is red is 26/52= 1/2. Given that, there are now 51 cards in the deck, 26 of them black. The probability the second card drawn is black is 26/51. The probability of "red, black" is (1/2)(26/51)= 13/51.

2) "black, black: There are 52 cards in the deck, 26 or them black. The probability the first card drawn is red is 26/52= 1/2. Given that, there are now 51 cards in the deck, 25 of them black. The probability the second card drawn is black is 25/51. The probability of "red, black" is (1/2)(25/51)= 25/102.

The probability of either "red, black" or "black, black", since those are mutually exclusive, is 13/51+ 25/102= 26/102+ 25/102= 51/102= 1/2!

a card is randomly selected from a deck of card. Find the probability that it is a black card or a face card

5 years ago

There are 52 cards in a deck in total. Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades). There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total). Diamonds and Hearts are red cards (there are 26 total red cards) and Clubs and Spades are black cards (there are 26 total black cards).

There are 26 black cards and 12 face cards in total. However, of those 26 black cards, there are 6 face cards. That means there are 26+12-6 = 32 cards in total that are either a black card or a face card, but not both. That means the answer to the question is 32/52 = 8/13.

Take this 5-min test to see how close you are to achieving your language learning goals.

5 years ago

A = number of black cards B = number of picture cards (or face cards) C = number of black picture cards

There are 26 black cards (spades and clubs), so A = 26.

There are 3 picture cards (Jack, Queen, King) in each suit. There are 4 suits (clubs, hearts, spades, diamonds). So there are 3*4 = 12 picture cards. This means B = 12

There are 2 suits which are black (spades and clubs) with 3 face cards per suit, so 2*3 = 6 cards which are both black cards and face cards. So C = 6

The number of cards that are either black cards or a face card, or both, is...

D = A+B-C D = 26+12-6

D = 32

So there are 32 cards that are either black cards or a face card, or both

This is out of 52 cards total, so

probability of selecting a black card or a picture card = D/52

probability of selecting a black card or a picture card = 32/52

probability of selecting a black card or a picture card = 8/13

The final answer, as a fraction, is 8/13

Find an online tutor for 1-on-1 lessons and master the knowledge you need! Prices from just $5 per hour.

Explore tutors