Question

The probability that it will rain on a particular day is $0.64$. What is the probability that it will not rain on that day?

Answer 1

Hint: We will use the statement that probability of happening of any event A and probability of not happening of that event sums up to be 1 i.e., $P\left( A \right) + P\left( {A'} \right) = 1$ to solve this question for the probability of not raining on a particular day.

Complete step-by-step answer:
We are given the probability that it will rain on a particular day. The probability is $0.64$.
We are required to calculate the probability that it will not rain on that day.
We know that if there is any event A and its probability of occurring is $P\left( A \right)$ and the probability that event A will not occur is $P\left( {A'} \right)$, then $P\left( A \right) + P\left( {A'} \right) = 1$.
So, let the event that it will rain on a particular day be A, then the probability that it will rain on that particular day will be $P\left( A \right)$.
$ \Rightarrow P\left( A \right) = 0.64$
The event that it will not rain on that day will be $A'$, then the probability that it will not rain on that day will be $P\left( {A'} \right)$.
Using the statement $P\left( A \right) + P\left( {A'} \right) = 1$ and putting the value of $P\left( A \right)$, we get
$
   \Rightarrow P\left( A \right) + P\left( {A'} \right) = 1 \\
   \Rightarrow 0.64 + P\left( {A'} \right) = 1 \\
   \Rightarrow P\left( {A'} \right) = 1 - 0.64 \\
   \Rightarrow P\left( {A'} \right) = 0.36 \\
 $
Therefore, the probability that it will not rain on the desired day is $0.36$.

Note: In this question, you may get confused in only the relation between the probabilities of happening and non – happening of any event. In mathematics, probability is defined as how likely any event is to happen in a desired manner. The sum of the probabilities of all possible outcomes of any event is always 1.