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Each card in a standard deck of 52 playing cards is unique and belongs to 111 of 444 suits:
13 cards are clubs
13 cards are diamonds
13 cards are hearts
13 cards are spades
Suppose that Luisa randomly draws 4 cards without replacement.
What is the probability that Luisa gets 2 diamonds and 2 hearts (in any order)?

Sagot :

facundo3141592

The probability that Luisa gets 2 diamonds and 2 hearts (in any order) is:

P = 0.022

How to get the probability?

The probability of getting a particular type of card, is given by the quotient between the number of cards of that type and the total number of cards.

Here, let's assume that the 4 draws are:

diamond-diamond-heart-heart.

In that order.

First, the probability of drawing a diamond card is equal to:

p₁ = 13/52

Because there are 13 diamond cards and 52 cards in total.

Bt after that draw, there will be 12 diamond cards and 51 cards in total, so the probability of getting the second diamond card is:

p₂ = 12/51.

Now, there are 13 heart cards and 50 cards in the deck, so the probability of getting the first heart card is:

p₃ = 13/50

And the probability of getting the second one is:

p₄ = 12/49.

The joint probability will be the product of the 4 individual probabilities, but we also need to take in account the possible permutations, these are:

(using D for diamond and H for heart).

D - D - H - H

D - H - D - H

D - H - H - D

H - D - D - H

H - D - H - D

H - H - D - D

So there are 6 permutations, this means that the probability is:

P = 6*p₁*p₂*p₃*p₄ = 6*(13/52)*(12/51)*(13/50)*(12/49) = 0.022

If you want to learn more about probability:

https://brainly.com/question/251701

#SPJ1

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