A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits (and, called 'hearts' and 'diamonds') are red, the other two (and, called 'spades' and 'clubs') are black. The cards in the deck are placed in random order (usually by a process called 'shuffling'). What is the probability that the first two cards drawn from the deck are both red

Question

Jonah

Mathematics

18 September, 03:22

A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits (and, called 'hearts' and 'diamonds') are red, the other two (and, called 'spades' and 'clubs') are black. The cards in the deck are placed in random order (usually by a process called 'shuffling'). What is the probability that the first two cards drawn from the deck are both red

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Jacobs · Answer 1

The probability that the first two cards drawn from the deck are both red is 24.51%

Step-by-step explanation:

A standard deck of cards has 52 cards. There are 4 of each card (4 Aces, 4 Kings, 4 Queens, etc.). There are 4 suits (Clubs, Hearts, Diamonds, and Spades) with each suit being 13 cards. Two of the suits (hearts and diamonds) are red, the other two (spades and clubs) are black.

P (first two cards drawn from the deck are both red) = P (First card is red) ∙ * P (Second card is red)

Since two suits of the card is red (i. e hearts and diamond) and each suit consist of 13 cards, the total number of red cad = 13 + 13 = 26

P (First card is red) = number of red card / total number of cards = 26 / 52

When the first card is drawn without replacement i. e the card is not put back into the deck, the total number of card reduces to 51 and the number of red card reduces to 25.

Therefore, P (Second card is red) = 25 / 51

P (first two cards drawn from the deck are both red) = P (First card is red) ∙ * P (Second card is red) = (26 / 52) * (25 / 51) = 0.2451 = 24.51%

The probability that the first two cards drawn from the deck are both red is 24.51%

Jovan · Answer 2

0.2451

Step-by-step explanation:

- A deck of card has a total of 52 cards. The number of black and red cards are equally divided:

Black cards = 26

Red cards = 26

- If we are to draw two cards from the deck of 52 cards. The probability of the first card drawn to be red would be:

P (1st Red) = Red cards / Total cards

= 26 / 52

- Once the first card is drawn we are left with 51 cards with the distribution of:

Black cards = 26

Red cards = 25

- The probability of second card drawn to be red from a deck of 51 cards would be:

P (2nd Red) = Red cards / Total cards

= 25 / 51

- So, the probability of drawing two red cards would be:

P (1st and 2nd red) = (26/52) * (25/51)

= 0.2451