﻿ A bag contains thirty marbles numbered from 1 to 30. Five marblesare drawn at random from the bag. T
X

### Question

A bag contains thirty marbles numbered from 1 to 30. Five marblesare drawn at random from the bag. There are a few ways to thinkabout 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, vemarbles are snatched up at once. c. Marbles are drawn one at a timewith replacement. Once a marble is drawn, it is tossed back intothe bag. Then the next marble is drawn, tossed back in, and soon.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!FOR EACH of these interpretations: (i) FOR EACH Describe the samplespace. How large is the set? (ii) FOR EACH What is the probabilitythat the marbles numbered 1 and 2 are not among those drawn fromthe bag? (iii) FOR EACH What is the probability that at least oneof the marbles numbered 16; 17; 18 are among the marbles drawn fromthe bag?

### Solution

xxxxx marbles xxx 30 xxxxxxxx xxxx xxx 30 .xx this x xxxxxxx xxxxx drawn xx the xxxxxx xxxxx xx 30c5=142506

a)marbles xxx drawn xxx xx x time xxxxxxx replacement xxxxxx*xxxx*xxxx*xxxx*xxxx=xxxxxxxxxxxxxxxxxxy xx xxxxxx/xxxxxxxx=x.xxxxx)xxxxx all xx once xxxxxxx xxxxxxxxxxx xxxxx that xxxxxxxxxxxxy is xx)xxx xx xxxxx with xxxxxxxxxxx means xxxx xx xx posibilitiesare x*xxxx=xxxxxxxxxxxxxy is xxx/xxxxxxxx=