Let $A = \{ \mathrm { H } , \mathrm { T } \}$ be the set of outcomes when a coin is tossed.
List the set of all outcomes of tossing a coin two times.

A) $( \mathrm { T } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { H } , \mathrm { H } )$
B) $( \mathrm { H } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { T } )$
C) $( \mathrm { H } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$
D) $( \mathrm { T } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { H } )$
E) $( \mathrm { T } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { T } )$

Question

Let $A = \{ \mathrm { H } , \mathrm { T } \}$ be the set of outcomes when a coin is tossed.  
List the set of all outcomes of tossing a coin two times.
 
A) $( \mathrm { T } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { H } , \mathrm { H } )$
B)   $( \mathrm { H } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { T } )$
C)   $( \mathrm { H } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$
D)   $( \mathrm { T } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { H } )$
E)   $( \mathrm { T } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { H } )$ , $( \mathrm { H } , \mathrm { T } )$ , $( \mathrm { T } , \mathrm { T } )$

Quizplus · Accepted Answer

Each outcome of tossing a coin twice can be represented as a pair, where the first element is the result of the first toss and the second element is the result of the second toss. Since there are two possible outcomes for each toss (H or T), there are $2 \times 2 = 4$ possible outcomes in total, which are all listed in option A: (T, T), (T, H), (H, T), and (H, H).

Let A={H,T}A = \{ \mathrm { H } , \mathrm { T } \}A={H,T}

Let $A = \{ \mathrm { H } , \mathrm { T } \}$