Question

Tossing a coin is an example of
A. Infinite discrete sample space
B. Finite sample space
C. Continuous sample space
D. None of these

Answer 1

Hint: 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 a number of outcomes which depends on the experiment.

Complete step by step answer:
Let us consider a sample space S it could be either continuous or discrete.
A sample space S can be
i) finite sample space.
ii) countably infinite sample space.
iii) uncountably infinite sample space.
A discrete sample space S is either finite or countably infinite. A continuous sample space S is uncountably infinite.
Now, getting back to our given question the event we have is tossing a coin.
A coin has two sides, heads and tails.
So, there are two possible outcomes of tossing a coin i.e, {head,tail}
From the definition of sample space we have that a sample space is the set of all possible outcomes.
Let the sample space here be denoted by S
S = {heads, tails}
Therefore, as there are two elements in our sample space which is finite it can be concluded that tossing a coin has a finite sample space.
Therefore, option B is correct.

Note:
Students might often get mistaken with their choice of answer as continuous sample space, but a continuous sample space is the space which is uncountably infinite. Sometimes, it can be mentioned in particular whether the coin is biased or unbiased and unbiased will be the same on both sides. Therefore if mentioned that an unbiased coin is given then the sample space would have one element.