Question

How many sample points are in the sample space when the coin is flipped \[4\] times?
\[\left( a \right)24 \\
\left( b \right)10 \\
\left( c \right)16 \\
\left( d \right)32\]

Answer 1

Hint: To solve the question, we consider the possible outcomes when the coin is tossed for once and then as it is flipped four times, so we find the total number of outcomes by raising the number of outcomes for flipping it once, to the power of four.

Formula used:
If a coin is tossed m times, then the total number of possible outcomes is
\[{{2}^{m}}\]
Wherec\[2\] is the number of outcomes when the coin is tossed only once.

Complete step by step solution:
Consider the case when a coin is tossed for once.We have the possible outcomes, i.e., \[\left\{ head,tail \right\}\]
So, the total number of outcomes are \[2\].Now as it is given in the question that the coin is flipped \[4\] times, thus, the total number of possible outcomes become,
\[{{2}^{4}}\]
Therefore, the number of possible outcomes when the coin is flipped \[4\] times is equal to \[16\].
Now each coin is equally likely to have the outcome \[\left\{ head,tail \right\}\], so for \[4\] times flipping, all the possible outcomes will be equally likely.Hence, the number of sample points that are in the sample space when the coin is flipped \[4\] times is \[16\].

Therefore, option \[\left( c \right)16\] gives the correct answer.

Note: In a probabilistic experiment, a sample point is the possible outcomes of the experiment. The set of all the sample points is called sample space. In this question, the set of all the sample points gives the total number of sample points as \[16\].