Question

What is the probability of getting exactly \[2\] tails?

Answer 1

Hint: The probability of an event is defined to be the ratio of the number of cases favourable to the event. i.e., the number of outcomes in the subset of the sample space defining the event to be the total number of cases. Probability means possibility. It is a branch of mathematics that deals with the occurrence of random events. The value of probability expressed from zero to one. Probability has been introduced in mathematics to predict how likely events are to happen.

Complete step-by-step answer:
When we flip the coin we have the favourable number $ n(S) = 1 $ , as we find only the probability of tail and total number $ n(A) = 2 $ , because a coin has two sides “Head” and “Tail”.
Therefore the probability of tail is $ P(A) = \dfrac{{n(S)}}{{n(A)}} $
 $ = \dfrac{1}{2} $
The probability of head = $ 1 - $ The probability of tail
\[ = 1 - \dfrac{1}{2}\]
 $ = \dfrac{1}{2} $
If we flip a coin for many times(or one time) then we get the probability of head is $ \dfrac{1}{2} $ and the probability of tail is $ \dfrac{1}{2} $ .
Therefore the probability of a tail is $ \dfrac{1}{2} $ .
From the given data if we get exact two tails then the probability of tails is
 $ P(A) = $ first time probability of tail $ \times $ second time probability of tail
We know every time when we flip the coin then the probability of tail is $ \dfrac{1}{2} $
  $ P(A) = \dfrac{1}{2} \times \dfrac{1}{2} $
 $ = \dfrac{1}{4} $
 $ = 0.25 $
So, the correct answer is “0.25”.

Note: Probability is widely used in all sectors in daily life like sports, weather reports, blood samples, congenital disabilities, statistics and many other sites. The probability formula provides the ratio of the number of favourable outcomes to the total number of possible outcomes. The probability of an event $ P(A) = \dfrac{{n(S)}}{{n(A)}} $ , where $ n(S) $ is the number of favourable outcomes and $ n(A) $ is the number of total outcomes.