Consider an urn containing 14 colored balls, of which 5 are white, 4 are black,
ID: 3150645 • Letter: C
Question
Consider an urn containing 14 colored balls, of which 5 are white, 4 are black, 3 are read, and 2 are green. A samole of 8 balls is taken. For the following, write out the formulations, but do not calculate them.
a) Suppose the sample is taken with replacement. What is the probability that the sample contains exactly 4 white, 2 black, 1 red and 1 green ball?
b) Suppose the sample is taken without replacement . What is the probability that the sample contains exactly 4 white, 2 black, 1 red and 1 green ball?
Explanation / Answer
Consider an urn containing 14 colored balls, of which 5 are white, 4 are black, 3 are read, and 2 are green. A sample of 8 balls is taken. For the following, write out the formulations, but do not calculate them.
a) Suppose the sample is taken with replacement. What is the probability that the sample contains exactly 4 white, 2 black, 1 red and 1 green ball?
Formulation
With replacement
Required probability = (4/14) * (2/14) * (1/14) * (1/14)
b) Suppose the sample is taken without replacement. What is the probability that the sample contains exactly 4 white, 2 black, 1 red and 1 green ball?
Formulation
Without replacement
Required probability = (4/14) * (2/10) * (1/9) * (1/8)