Question

Probability of getting 3 heads and 3 tails in tossing a coin 3 times is
A.\[\dfrac{1}{8}\]
B.\[\dfrac{1}{4}\]
C.\[\dfrac{3}{8}\]
D.\[\dfrac{1}{2}\]

Answer 1

Hint: Here, we will find the sample space when a coin is tossed three times. This will give us the total number of possible outcomes. Then we will find the favorable outcomes of getting 3 heads and 3 tails and then find the respective probability using the formula of probability. We will add both the probabilities together to get the required probability

Formula Used:
Probability \[ = \] Number of favorable outcomes \[ \div \] Total number of outcomes

Complete step-by-step answer:
We know that, when a coin is tossed one time then, the sample space is \[\left\{ {H,T} \right\}\].
This means that we can get either a head or a tail when a coin is tossed once.
Now, since the coin has been tossed 3 times, hence
The total number of possible outcomes \[ = {2^3} = 8\]
This is because of the fact that when a coin is tossed \[n\] number of times, then the total possible outcomes are \[{2^n}\].
Hence, sample space, \[S = \left\{ {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} \right\}\]
$\therefore $ Total number of possible outcomes\[ = 8\]
Now, we are required to find the probability of getting 3 heads and 3 tails.
Here, we can observe that
The favorable outcomes of getting 3 heads \[ = \left\{ {HHH} \right\} = 1\]
The favorable outcomes of getting 3 tails \[ = \left\{ {TTT} \right\} = 1\]
We know that, Probability, \[ = \] Number of favorable outcomes \[ \div \] Total number of outcomes
Therefore, the probability of getting 3 heads when 3 coins are tossed \[ = \dfrac{1}{8}\]
And, the probability of getting 3 tails when 3 coins are tossed \[ = \dfrac{1}{8}\]
Now we will find the required probability by adding all the probabilities. Therefore,
The total probability \[ = \dfrac{1}{8} + \dfrac{1}{8}\]
Adding the terms, we get
\[ \Rightarrow \] The total probability \[ = \dfrac{2}{8} = \dfrac{1}{4}\]
Hence, the required probability of getting 3 heads and 3 tails in tossing a coin 3 times is \[\dfrac{1}{4}\].
Therefore, option B is the correct answer.

Note: Probability tells us the extent to which an event is likely to occur, i.e. the possibility of the occurrence of an event. Hence, it is measured by dividing the favorable outcomes by the total number of outcomes. Probability of an event varies from 0 to 1 that is it cannot be less than 0 or greater than 1. If the probability is 1 then the event is called a sure event, whereas the event with 0 probability never occurs.