a. [tex]S_1 = \{1,2,3,4,5,6\}[/tex]
b. [tex]S_2=\{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z\}[/tex]
c. [tex]S_3 = \{HH, HT, TH, TT\}[/tex]
d. [tex]S_4 =\{1T,2T,3T,4T,5T,6T,1H,2H,3H,4H,5H,6H\}[/tex]
Step-by-step explanation:
We will write the sample space of all options one by one.
a. Rolling a 6 sided die
As the die has six sides numbered from 1 to six then the sample space will be:
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
b. Guessing the first initial of a student's name:
As the English language has 26 alphabets, the first initial can be any alphabet so the sample space will be all letters:
[tex]S_2=\{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z\}[/tex]
c. Tossing two coins
As two coins are tossed, the outcomes will be a combination of two outcomes
[tex]S_3 = \{HH, HT, TH, TT\}[/tex]
d. Rolling a 6 sided die and tossing a coin
As the die is rolled and then a coin is tossed. The die's coin will either combine with heads or tails
So,
[tex]S_4 =\{1T,2T,3T,4T,5T,6T,1H,2H,3H,4H,5H,6H\}[/tex]
Hence,
a. [tex]S_1 = \{1,2,3,4,5,6\}[/tex]
b. [tex]S_2=\{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z\}[/tex]
c. [tex]S_3 = \{HH, HT, TH, TT\}[/tex]
d. [tex]S_4 =\{1T,2T,3T,4T,5T,6T,1H,2H,3H,4H,5H,6H\}[/tex]
Keywords: Sample Space, Probability
Learn more about sample space at:
- brainly.com/question/11007026
- brainly.com/question/11207748
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