Question

A coin is tossed $300$ times and we get head: $136$ times and tail: $164$ times. When a coin is tossed at random, what is the probability of getting a tail?

Answer 1

Here, we will find the number of outcomes favourable to the required event. Then, we will use the formula of probability to find the probability of getting a tail. Probability is defined as the certainty of occurrence of an event at random.

Formula used:
If $A$ is an event, then $P(A) = \dfrac{{n(A)}}{{n(S)}}$, where $n(A)$ is the number of outcomes favourable to the event $A$ and $n(S)$ is the total number of outcomes in the sample space i.e., the number of all possible outcomes.

Complete step by step solution:
We know that when a coin is tossed, there are only two possible outcomes which are Head and Tail. We are given that a coin is tossed $300$ times are the number of occurrences of a Head are $136$ and those of a Tail are $164$. We have to find the probability of getting a Tail. This means that during a random toss, we have to find the chances of a Tail occurring.
Let $T$ be the event of getting a tail. Then, $n(T) = 164$, which is given. Also, $n(S) = 300$ which are the total number of tosses.
Therefore, the probability of getting a tail is
$P(T) = \dfrac{{n(T)}}{{n(S)}} = \dfrac{{164}}{{300}}$
We will now divide the numerator and denominator by the common factor, 4. Hence, we get the probability as
$\Rightarrow P(T) = \dfrac{{41}}{{75}}$

Therefore, the probability of getting a tail is $\dfrac{{41}}{{75}}$.

Note:
We need to keep in mind that the probability of any event is always a value that lies between 0 and 1. The probability of an impossible event is 0, whereas the probability of a sure event is 1. Also, if $\overline A$ is even complementary to the event $A$, then $P(A) + P(\overline A ) = 1$. In the given problem, the event that is complementary to getting a Tail is the event of getting a Head.