Question

Write the sample space of the experiment of tossing two coins. Write n(S) also.

Answer 1

Hint: When a coin is tossed, the possible outcomes are head and tail .Here, we denote Head with ‘H’ and tail with ‘T’. We have already studied that the number of elements in sample space if a coin is tossed ‘n’ times is n(S) = \[{2^n}\] .
We use the above mentioned formula in this question to derive the answer.

Complete step-by-step answer:
The experiment in this question is tossing a coin twice.
We considered that Heads are represented by ‘H’ and tails are represented by ’T’.
Number of elements in the sample space if a coin is tossed twice is n(S) =\[{2^2}\]
\[ \Rightarrow {2^2} = 4\]
The elements in sample space are two heads on 2 coins, two tails on two coins, a head on first coin and a tail on second coin and a tail on first coin and a head on second coin .This format is represented as
{HH, TT, HT, TH}.
Hence the sample space of an experiment of tossing a coin twice is {HH, TT, HT, TH}.

Note: The sample space of an experiment or an event is defined as a set of possible outcomes of that event. The sample space of an experiment is represented by a letter “S” and the number of elements in sample space is represented by n(S). While writing a sample set of an experiment flower brackets shall be used \[\left( {\{ \} } \right)\] and all the elements shall be separated by comma (,).