Question

Write the sample space for the experiment of tossing a coin four times.

Answer 1

Hint:When a coin is tossed, we can get two sample space: one is head, and another is tail. But when a coin is tossed four times, we can get several options.
We know that, if a coin is tossed for \[n\] times, the number of sample space is \[{2^n}\].

Complete step-by-step answer:
The given experiment is tossing a coin for four times.
There are only two sides of a coin: head and tail.
Here, we denote head as \[H\] and tail as \[T\].
We know that, if a coin is tossed for \[n\] times, the number of sample space is \[{2^n}\].
Here, the coin is tossed for \[4\] times, the number of sample space is \[{2^4} = 16\]
When a coin is tossed for four times, the sample space can be written as:
\[
  \{ HHHH,HTHH,THHH,HTHT, \\
  HHHT,HTTH,TTHH,THTH, \\
  HHTT,HHTH,TTTH,THHT, \\
  HTTT,TTTT,TTHT,THTT\} \\
 \]
Hence, the sample space for the experiment of tossing a coin four times is \[
  \{ HHHH,HTHH,THHH,HTHT, \\
  HHHT,HTTH,TTHH,THTH, \\
  HHTT,HHTH,TTTH,THHT, \\
  HTTT,TTTT,TTHT,THTT\} \\
 \]

Note:A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “\[S\]”. The subset of possible outcomes of an experiment is called events. A sample space may contain several outcomes which depends on the experiment. If it contains a finite number of outcomes, then it is known as discrete or finite sample spaces.The sample space for a random experiment is written within curly braces “{} “.