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.
30% of 10 is 3. So there are 3 black balls and 7 white balls.
a. How many possible samples are there?
10 balls Choose 5 = 10C5 = 252 samples
b. How many of these samples will contain no black balls?
7 white balls Choose 5 = 7C5 = 21
How many will contain exactly one black ball?
That's 1 black ball and 4 white balls.
(3 back balls Choose 1)(7 white balls Choose 4) = (3C1)(7C4) =
(3)(35) = 105
How many will contain 2?
That's 2 black ball and 3 white balls.
(3 back balls Choose 2)(7 white balls Choose 3) = (3C2)(7C3) =
(3)(35) = 105
Three?
That's 3 black balls and 2 white balls.
(3 back balls Choose 3)(7 white balls Choose 2) = (3C3)(7C2) =
(1)(21) = 21
Four?
None, for there are only 3 black balls
Five?
Also none, for there are only 3 black balls
c. Can you relate the results to probabilities?
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
