# Discrete Mathematics Marble Probability Problem

A bag contains thirty marbles numbered from 1 to 30. 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. That is, once a marble is drawn, it is not replaced in the bag.

b. Marbles are drawn all at once without replacement. That is, five marbles are snatched up at once.

c. Marbles are drawn one at a time with replacement. Once a marble is drawn, it is tossed back into the bag. Then the next marble is drawn, tossed back in, and so on. For each of these interpretations,

(i) Describe the sample space. How large is the set?

(ii) What is the probability that the marbles numbered 1 and 2 are not among those drawn from the bag?

(iii) What is the probability that at least one of the marbles numbered 16,17,18 are among the five marbles drawn from the bag?

• for the sample spaces I have:

A.) $$P(30,5)$$

B.) $$C(30,5)$$

C.) $$30^5$$

• for the probability of marbles 1 and 2 not being chosen I have:

A.) $$\dfrac{P(28,5)}{P(30,5)}$$

B.) $$\dfrac{C(28,5)}{C(30,5)}$$

C.) $$\dfrac{28^5}{30^5}$$

• and then for part (iii) I really have no idea

Any help is appreciated thank you!

• You have only given the sizes of the respective sample spaces. "Description" means you also have to provide the description of the set which serves as a sample space, not merely its size. However, the second part is fine. – астон вілла олоф мэллбэрг Nov 30 '18 at 3:46
• Please read this tutorial on how to typeset mathematics on this site. – N. F. Taussig Nov 30 '18 at 11:58

and note that exactly one of the above events must occur. That is, $$\Pr(\text{at least one of }16,17,18\text{ drawn})+\Pr(\text{none of }16,17,18\text{ drawn})=1\text{,}$$ for any of the scenarios.