Question

# The probability that it rains tomorrow is 0.35. Work out the probability that it does not rain tomorrow.

Hint: In order to solve this particular question of probability, we need to follow some of the rules of probability, to get to our final result. Those rules are:-
Probability Rule 1:-
For any event A, 0 ≤ P(A) ≤ 1.
Probability Rule 2:-
The sum of the probabilities of all possible outcomes is 1.
We can also solve this question by following the probability rule 2, which says the sum of probabilities of all possible outcomes is 1. So, according to this rule, the sum of the probability that it may rain tomorrow and the probability that it does not rain tomorrow is equal to 1.

Complete step by step solution: Let the event that it will rain tomorrow be indicated with ‘E’.
So,the probability that it may rain tomorrow is $\text{P}\left( \text{E} \right)=0.35$ ……..given
We are asked for the probability that it does not rain tomorrow, so we get;
\begin{align} & \text{P}\left( {{\text{E}}^{'}} \right)=1-\text{P}\left( \text{E} \right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left[ \because \ P\left( E \right)+P\left( E' \right)=1 \right] \\ & \Rightarrow \text{P}\left( \text{E }\!\!'\!\!\text{ } \right)=1-0.35 \\ \end{align}
$\Rightarrow\text{P}\left(\text{E}^{'}\right)=0.65$

Therefore, the probability that it does not rain tomorrow is 0.65.

Note: The formula of the probability of an event is:
P(A) $=\dfrac{n(E)}{n(S)}$
Where,
P(A) is the probability of an event “A”
n(E) is the number of favourable outcomes
n(S) is the total number of events in the sample space.
Here, the favourable outcome means the outcome of interest.
Sometimes, students get confused about the word “favourable outcome” with “desirable outcome”. In some of the requirements, losing in a certain test or occurrence of an undesirable outcome can be a favourable event for the experiments run.