# Two cards are drawn from a well-shuffled pack of 52 cards. Find the probability distribution of the number of aces.

In a deck of 52 cards, there are 4 aces each of one suit respectively.

Let X be the random variable denoting the number of aces for an event when two cards are drawn simultaneously.

X can take values 0, 1 or 2.

P(X = 0) =

[For selecting 0 aces, we removed all 4 aces from the deck and selected out of 48]

P(X = 1) =

[For selecting 1 ace, we need to select and 1 out of 4 and not any other]

P(X = 2) =

[For selecting 2 aces, we need to select and 2 out of 4]

Now we have pi and xi.

As

Thus, ∑(pi) = 1

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

The following table gives probability distribution:

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