You select a card from a standard shuffled deck of 52 cards. Without replacing, you select another card. Find the probability that you select a black card, then a red card.

Question

the answer has to be in a fraction

Answer 1

A standard deck (52 cards, no jokers) has 26 black and 26 red cards. Thus, on the first draw, the odds of getting black are 1/2.

For the second draw, there are now 25 black and 26 red, for a total of 51. The odds of drawing red are 26/51

So, the combined probability is 1/2 * 26/51 = 13/51

Answer 2

There are 26 red cards and 26 black cards in the deck of 52 total cards.

First draw: The probability of selecting a black card is 26/52

Second draw: The probability of selecting a red card is 26/51.

The probability of both events happening is 26/52 times 26/51 or 676/2652 or (reduced) 13/51

Answer 3

This one is dependent probability, each time you remove a card without replacing it back in the deck you change the total population with respect to the distribution and ratios

In a typical deck of cards there are 26 black cards and 26 red cards.

Your first draw A consists of a full deck with a total population of 52 cards so your first draw is

26 out of 52 or 26/52

26/52 is 1/2

Since you don't put the first card back, you now have a total population of 51 cards to draw from 25 of them are black because you took one out and 26 are red, so the second draw B will be based on

26 out 51

26/51

Now the probability that both will occur is P(A and B) = P(A) *P(B after A)

1/2 *26/51 = 26/102 this reduces to 13/51

I hope you find this useful if you have any questions please send me a message.

Answer 4

Hello Kathia,

Half of the deck is black, and half of the deck is red.

So P(Black) = 26/52 = 1/2.

Since the card is not replaced, there are now only 51 cards in the deck, but still 26 red cards

→ P(Red) = 26/51.

Therefore, the probability of drawing a black, followed by a red is

P(Black) * P(Red) = (1/2) * (26/51) = 13/51.

I hope the above helps, and thank you for the question.

Michael E.

Answer 5

Getting black card probability is 26/52 (there are 26 black cards in the deck of cards)

Getting red card after that is 26/51 (now there are only 51 card left)

So the combined probablity is 26/52 * 26/51