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:
