Question

The probability that it will be sunny tomorrow is 0.97. Work out the probability that it will not be sunny tomorrow.

Answer 1

Hint: Denote the given event by E and then the probability of that event not happening needs to be calculated. For that use the formula, $P\left( E \right) + P\left( {{\text{not }}E} \right) = 1$ and make the substitution of the probability of the event happening, that is, the day being a sunny day. Solve the obtained equation to find the required value.

Complete step-by-step answer:
We begin our solution by considering what is given to us. It is given to us that the probability that it will be a sunny day tomorrow is 0.97.
So, let the event E be the day being sunny.
Thus, we have;
$P\left( E \right) = 0.97$
It is known to us that the sum of probability of any event happening and the probability of that event not happening is equal to 1.
Thus,
$P\left( E \right) + P\left( {{\text{not }}E} \right) = 1$ ……(1)
Here, it is clear to us that the “Not E” means that the day is not sunny.
So, all we need to do is to calculate the value of $P\left( {{\text{not }}E} \right)$.
For that, substitute the value of $P\left( E \right) = 0.97$ in equation (1) as follows;
$
  0.97 + P\left( {{\text{not }}E} \right) = 1 \\
   \Rightarrow P\left( {{\text{not }}E} \right) = 1 - 0.97 \\
   \Rightarrow P\left( {{\text{not }}E} \right) = 0.03 \\
 $
Hence, the probability that it will not be sunny tomorrow is 0.03.

Note: While applying the formula for the probability, given by; $P\left( E \right) + P\left( {{\text{not }}E} \right) = 1$, you need to be sure that the events are not inclusive events, meaning, that you need to be sure about the fact that both the events given to you cannot happen at the same time. As a day either be a sunny day or it cannot be a sunny day, at one particular time, thus we have used the mentioned formula to find the required value.