Question 1088141
Consider an urn containing black and white balls of which 30% are 
black.  A simple random sample of five balls is taken. Suppose that 
the urn contains 10 balls.
<pre>
30% of 10 is 3.  So there are 3 black balls and 7 white balls.
</pre>
a. How many possible samples are there? 
<pre>
10 balls Choose 5 = 10C5 = 252 samples
</pre>
b. How many of these samples will contain no black balls? 
<pre>
7 white balls Choose 5 = 7C5 = 21
</pre>
How many will contain exactly one black ball? 
<pre>
That's 1 black ball and 4 white balls.

(3 back balls Choose 1)(7 white balls Choose 4) = (3C1)(7C4) = 
(3)(35) = 105
</pre>
How many will contain 2? 
<pre>
That's 2 black ball and 3 white balls.

(3 back balls Choose 2)(7 white balls Choose 3) = (3C2)(7C3) = 
(3)(35) = 105
</pre>
Three? 
<pre>
That's 3 black balls and 2 white balls.

(3 back balls Choose 3)(7 white balls Choose 2) = (3C3)(7C2) = 
(1)(21) = 21
</pre>
Four?
<pre>
None, for there are only 3 black balls
</pre>
Five? 
<pre>
Also none, for there are only 3 black balls
</pre>
c. Can you relate the results to probabilities?
<pre>
P(no black balls) = 21/252 = 1/12
P(1 black ball) = 105/252 = 5/12
P(2 black balls) = 105/252 = 5/12
P(3 black balls) = 21/252 = 1/12
P(4 black balls) = 0/252 = 0
P(5 black balls) = 0/252 = 0

Edwin</pre>