a. {1,2,3,4,5,6}
b. {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}
c. {HH,HT,TH,TT}
d. {1T,2T,3T,4T,5T,6T,1H,2H,3H,4H,5H,6H}
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:
S1 = {1,2,3,4,5,6}
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:
S2 = {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}
c. Tossing two coins
As two coins are tossed, the outcomes will be a combination of two outcomes
S3= {HH,HT,TH,TT}
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,
S4 = {1T,2T,3T,4T,5T,6T,1H,2H,3H,4H,5H,6H}
Hence,
a. {1,2,3,4,5,6}
b. {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}
c. {HH,HT,TH,TT}
d. {1T,2T,3T,4T,5T,6T,1H,2H,3H,4H,5H,6H}
Keywords: Sample Space, Probability
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