: Four cards are drawn without replacement from a well shuffled standard deck of cards. Let X be the number of aces drawn.

Question

12. What are the possible values of the random variable X? Write them in increasing order as a set using roster (or list) notation.
13. Sketch a histogram for the probability distribution of the variable X.
14. What is the expected value of X?

Here are the answers I came up with but I would like to know if they are correct. If they are correct, can you direct me on how to plot the histogram.

P(x=0)= 0.7187

P(x=1)= .6388

P(x=2)= .0041

P(x=3)=.0001773

P(x=4)=.0000003737

Answer 1

I know some or even all of your answers must be wrong, since the sum of all the prob's has to add up to 1
The sum of your first 2 results is already over 1

first one is correct,
I assume you did
C(48,4) /C(52,4) = .718736..

Doing the 2nd the same way
you want to chose 1 ace from the 4 aces, then 3 of the remaining 48 non-aces
= C(4,1) x C(48,3) / C(52,4) = .2556

3rd:
2 aces, 2 non-aces

prob(x=2) = C(4,2) x C(48,2)/C(52,4) = .0250

complete the remaining two, using the same procedure
Check to see if the sum of all results = 1