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

Hint:
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.