The probability that Luisa gets 2 diamonds and 2 hearts (in any order) is:
P = 0.022
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:
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