SOLUTION: Three cards are drawn from a deck without replacement. The number of aces is counted. The expected value of the random variable in the experiment is: A. 1 B. 1.0134 C. .2308

X = no. of aces drawn which can either be 0, 1, 2, or 3.

So make this chart:



Now we must calculate the probabilities to go in
the bottom row of the chart.

We first calculate the probability of getting 0 aces.
This means we draw 3 non-aces.  There are 48 non-aces.
So the number of ways to choose three non-aces is


The denominator is 

So the probability of getting 0 aces is 

Next we calculate the probability of getting 1 ace.
This means we draw 2 non-aces and 1 ace. There are 
48 non-aces. So the number of ways to choose two 
non-aces is  and the number of ways to
choose the ace is  ways.  That's 
 ways.

The denominator again is 

So the probability of getting exactly 1 ace is 


Next we calculate the probability of getting 
exactly 2 aces. This means we draw 1 non-ace and 
2 ace3. There are 48 non-aces. So the number of 
ways to choose one non-aces is  and 
the number of ways to choose 2 aces is  
ways.  That's 
 ways.

The denominator is as before 

So the probability of getting exactly 2 aces is 


Finally we calculate the probability of getting 3 aces.
The number of ways to choose 3 aces is  ways.  

The denominator is 

So the probability of getting exactly 3 aces is 


So we fill in the chart:

 

Now to find the expectation, we add the products of each
value of x times its probability:



That rounds to choice C, 

Edwin