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Here is a table showing all 52 cards in a standard deck.
Face cards
Color Suit Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King
Red Hearts 1 2 3 4 5 6 7 8 9 10 JK
Red Diamonds 2 3 4 6. 7 8. 9. 10. J. e. K.
Black Spades 4 24 36 46 54 64 74 8. 9. 10. J . K
Black Clubs 44 24 3 44 5% 6% 74 84 94 104 Jo 04 K
A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the
deck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck.
What is the probability that all three of the cards are red?
Do not round your intermediate
computations. Round your final answer to four decimal places.

Here Is A Table Showing All 52 Cards In A Standard Deck Face Cards Color Suit Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King Red Hearts 1 2 3 class=

Sagot :

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We want to find the probability of drawing 3 red cards from a deck of 52 cards.

We will find that the probability is P = 0.1176

Let's see how to get that probability.

We know that a standard deck of 52 cards has:

  • 26 red cards
  • 26 black cards

And we assume that all the cards have the same probability of being drawn. Then the probability of drawing a red card in the first draw is just the quotient between the number of red cards and the total number of cards, we get:

p₁ = 26/52

For the second draw, we compute the probability in the same way, but now there are 25 red cards in the deck and 51 cards in total (because one is already drawn). Then the probability in this case is:

p₂ = 25/51

Finally, for the third card, we have 24 red cards and 50 total cards, then the probability will be:

p₃ = 24/50

The joint probability (the probability of drawing the 3 red cards in the same event) is the product of the individual probabilities.

P = p₁*p₂*p₃ = (26/52)*(25/51)*(24/50) = 0.1176

If you want to learn more, you can read:

https://brainly.com/question/10224828

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