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# Two cards are drawn simultaneously from a well-shuffled deck of 52 cards. Find the probability distribution of the number of successes, when getting a spade is considered a success.

In a deck of 52 cards, there are 13 spades.

Let X be the random variable denoting the number of success and success here is getting a spade for an event when two cards are drawn simultaneously.

We can say that the number of successes is equal to some spades obtained in each draw.

X can take values 0, 1 or 2.

P(X = 0) =

[For selecting 0 spades, we removed all 13 spades from the deck and selected out of 39]

P(X = 1) =

[For selecting 1 spade, we need to select and 1 out of 13 spade and not any other spade]

P(X = 2) =

[For selecting 2 spades, we need to select and 2 out of 13 spades]

Now we have pi and xi.

Now we are ready to write the probability distribution for X:-

The following table gives probability distribution:

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