Answer to Question #225193 in Statistics and Probability for Reyad

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

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