Question

What is the probability of getting exactly $3$ tails

Answer 1

Hint : In the given question we have to collect the favorable number of outcomes from the sample space of tossing the three coins . After getting the favorable outcomes we will use the formula $P\left( E \right) = \dfrac{{favorable{\text{ outcomes}}}}{{Total{\text{ number outcomes}}}}$ for getting the required probability , where $\left( E \right)$ is the event occurred .

Complete step-by-step answer :
In this question we will consider that $3$ coins to be tossed simultaneously .
Let $\left( E \right)$ be the event of tossing the coins .
So , the sample space for $3$ coins to be tossed simultaneously will be given as :
S = \left\\{ {HHH,HHT,HTH,THH,TTT,TTH,THT,HTT} \right\\} . Therefore , we have total $8$ outcomes .
From the above sample space we have to look for the favorable outcome . So , on observing we get only one outcome as favorable .
Therefore , the number of favorable outcomes will be $= 1$ .
The required probability of getting exactly $3$ tails will be
$P\left( E \right) = \dfrac{{favorable{\text{ outcomes}}}}{{Total{\text{ number outcomes}}}}$
On putting the values we get ,
$P\left( E \right) = \dfrac{1}{8}$ .
Therefore , the required probability is $\dfrac{1}{8}$.

Note : The set of all the possible outcomes of a random experiment is called the sample space associated with it and it is generally denoted by $S$ . If a random experiment is performed , then each of its outcomes is known as elementary events also known as possible outcomes . Probability is a measure of the likeliness of an event to occur. Many events that cannot be predicted with total certainty , in that event we can predict only the chance of an event to occur i.e. how likely they are to happen, using probability . Probability can vary from 0 to 1 , where 0 means the event to be an impossible one and 1 indicates a certain event .