Question

A coin is tossed $ 100 $ times with the following frequencies: $ Head:20 $ . Find the probability for events having heads only.
a) $ 0.2 $
b) $ 0.5 $
c) $ 0.65 $
d) $ 1.5 $

Answer 1

Hint: First, we need to analyze the given information carefully so that we are able to solve the problem. Here, we are given a probability consisting of an experiment. The experiment is tossing a coin $ 100 $ times. The given outcome is getting heads $ 20 $ times. We are asked to calculate the probability for the event having heads only.
     We need to use the formula of the probability of an event in this question so that we can easily obtain the desired result.
Formula to be used:
  The formula to calculate the probability of an event is as follows.
The probability of an event (say A), $ P\left( A \right) = \dfrac{{number{\text{ }}of{\text{ }}favorable{\text{ }}outcomes}}{{total{\text{ }}number{\text{ }}of{\text{ }}outcomes}} $

Complete step by step answer:
 The given experiment is tossing a coin $ 100 $ times and the outcome is getting head $ 20 $ times.
While tossing a coin, we get both head and tail.
Since the coin is tossed for $ 100 $ times, the total number of outcomes will be $ 100 $ .
Since we get head $ 20 $ times, the number of favorable outcomes will be $ 20 $ .
We are asked to calculate the probability of getting head.
Let $ P\left( H \right) $ be the probability of getting head.
Now, we shall use the probability of an event formula.
The formula to calculate the probability of an event is as follows
The probability of an event (say A), $ P\left( A \right) = \dfrac{{number{\text{ }}of{\text{ }}favorable{\text{ }}outcomes}}{{total{\text{ }}number{\text{ }}of{\text{ }}outcomes}} $
Hence, the probability of getting head, $ P\left( H \right) = \dfrac{{number{\text{ }}of{\text{ }}favorable{\text{ }}outcomes}}{{total{\text{ }}number{\text{ }}of{\text{ }}outcomes}} $
 $ \Rightarrow P\left( H \right) = \dfrac{{20}}{{100}} $
 $ \Rightarrow P\left( H \right) = \dfrac{1}{5} $
 $ \Rightarrow P\left( H \right) = 0.2 $
Therefore, the probability of getting head is $ 0.2 $

So, the correct answer is “Option a”.

Note: The probability of an event is nothing but the ratio of the number of favorable outcomes and the total number of outcomes. This is given by the formula $ P\left( A \right) = \dfrac{{number{\text{ }}of{\text{ }}favorable{\text{ }}outcomes}}{{total{\text{ }}number{\text{ }}of{\text{ }}outcomes}} $ .
Hence, we got the required probability of getting head.