Question

A weather forecast says that there is a 40% chance of rain. How do I find the odds against rain?

Answer 1

Hint: For this type of question stated above we can easily see that this is a type of probability in which we know the probability of success and we are asked to find the probability of failure for which we will be using the relation p (success) + p (failure) = 1.

Complete step-by-step solution:
For the above stated question it is stated that the weather forecast says that there is a chance of 40% raining which means that the probability that there will be rainfall is 40%.
We will assume that probability of success is that rainfall is going to take place and from the above question we can clearly say that the probability of success i.e. p (success) = probability that rainfall is going to take place
So, now we can say that p (success) = 40%.
Now there is a rule in overall probability is the sum of probability of success and probability of failure which means that
Probability (P) = p (success) + p (failure)…….. (1)
We also know that probability can have a maximum value of one (1) and when it is stated in percentage it can also be said as 100%.
So, now when we see the question we can see that, we already know p(success) and Probability(P) and we need to find the value of p(failure) which signifies that rainfall is not going to take place.
To find the value of p (failure), we will substitute the known values in equation (1) and then we will get the answer for p (failure), so on substituting we get,
\[\begin{align}
  & \Rightarrow 100=40+\text{p}\left( \text{failure} \right) \\
 & \Rightarrow \text{p}\left( \text{failure} \right)=60 \\
\end{align}\]
So from the above solution we can easily say that the probability that rainfall is not going to take place or odds against rain is 60%.

Note: The common mistake that is done in this type of question is to not notice when or what to take in the field of success or failure, so to simplify success defines whether the probability of that substance is going to happen like in the above question, rainfall is going to happen so that is p(success) and against rain which becomes p(failure).