Question

The number of possible outcomes when a coin is tossed $6$ times is?
A. $36$
B. $64$
C. $12$
D. $32$

Answer 1

For this problem we need to calculate the number of possible outcomes for the given event. We have given the event that is tossing a coin. So, we will first write the possible outcomes when the coin is tossed one time. After that we will calculate the number of possible outcomes when the coin is tossed two times. Likewise, we will continue up to the event when the coin is tossed six times and there, we will end our solution with the calculated outcomes as the required solution.

Complete step by step solution:
Given event is tossing a coin.
We know that when we toss a coin, we can have possibly two outcomes which are Head and Tail.
Hence the total number of outcomes when the coin is tossed one time is $2$.
Now the coin is tossed again that means the total number of outcomes in this event is equal to the number of possible outcomes of previous event times or number of possible outcomes when the coin is tossed one time. Mathematically we can write it as
$\Rightarrow 2\times 2=4$
Hence the total number of outcomes when the coin is tossed two times is $4$.
Again, the number of possible outcomes when the coin is tossed three times is given by $4\times 2=8$.
Similarly, we can write
Possible outcomes when coin is tossed four times is $8\times 2=16$
Possible outcomes when the coin is tossed five times is $16\times 2=32$.
Possible outcomes when the coin is tossed six times is $32\times 2=64$.
Hence the required answer which is the total number of outcomes when the coin is tossed six times is $64$.

Note: On observing the above values we can simply write the number of possible outcomes when a coin is tossed $n$ times as ${{2}^{n}}$. We can also use this formula for this solution by substituting $n=6$, then we will get
$\begin{aligned} & \Rightarrow {{2}^{n}}={{2}^{6}} \\\ & \Rightarrow {{2}^{n}}=64 \\\ \end{aligned}$
From both the methods we got the same result.