Question

A bag contains 20 marbles. These marbles are identical, except they are labeled with the integers 1 through 20. Five marbles are drawn at random from the bag. There are a few ways to think about this.
a. Marbles are drawn one at a time without replacement. Once a marble is drawn, it is not replaced in the bag. We consider all the lists of marbles we might create. (In this case, picking marbles 1, 2, 3, 4, 5 in that order is different from picking marbles 5, 4, 3, 2, 1.)
b. Marbles are drawn all at once without replacement. Five marbles are snatched up at once. (In this case, picking marbles 1, 2, 3, 4, 5 and picking marbles 5, 4, 3, 2, 1 are considered the same outcome.)
c. Marbles are drawn one at a time with replacement. Once a marble is drawn, it is tossed back into the bag (where it is hopelessly mixed up with the marbles still in the bag). Then the next marble is drawn, tossed back in, and so on. (In this case, picking 1, 1, 2, 3, 5 and picking 1, 2, 1, 3, 5 are different outcomes.)

Required:
For each of these interpretations, describe the sample space that models these experiments.

Answer 1

Answer:

a. The probability of getting an specific sequence would be

$(1/20)*(1/19)*(1/18)*(1/17)*(1/16)$

b. The probability  of having an specific sequence would be.

$5/20 = 1/4$

Step-by-step explanation:

a. If you draw 5 marbles without replacement, the probability of getting an specific sequence would be

$(1/20)*(1/19)*(1/18)*(1/17)*(1/16)$

b. If you draw 5 marbles all at once without replacement, the probability  of having an specific sequence would be.

$5/20 = 1/4$