Question

55 students are selected at random from an engineering class and classified as

male or female. List the elements of sample space S1 using the letter M for male

F for female. Define a second sample space S2 Where the elements represent the

number of females selected.

Answer 1

$$S_1 = \{55\ times\ M\&0\ times\ F, 55-1\ times\ M\&1\ times\ F,$$

$$55-2\ times\ M\&2\ times\ F, ...,$$

$$1\ times\ M\& 55-1\ times\ F,0\ times\ M\& 55\ times\ F\}$$

$$S_1 = \{55\ times\ M\&0\ times\ F,54\ times\ M\&1\ times\ F,$$

$$53\ times\ M\&2\ times\ F, ...,$$

$$1\ times\ M\& 54\ times\ F,0\ times\ M\& 55\ times\ F\}$$

Because $a$ students are selected at random, the number of selected female students can be $0,1,..., 55-1, 55,$ then the sampe space $S_2$ is

$$S_1 = \{0,1,2,..., 54, 55\}$$