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

Let the event that it will be a sunny day tomorrow be X and we are required to find the probability that the event E does not happen.
To do so, we will take the help of the formula $P(X) + P(\overline X ) = 1$ and substitute the probability of the event that the day will be a sunny day in the given formula.
Thus, solve the above equation to get the required probability.

Complete step by step solution:
Let the event that it will be a sunny day tomorrow be X. Also, it is given that the probability that it will be sunny tomorrow is 0.97.
$\therefore P(X) = 0.97$
Now, we know that the sum of probability of any event happening and the probability of that same event not happening is 1 i.e. $P(E) + P(\overline X ) = 1$ … (1)
Here, it is clear that the symbol $\overline X$ defines that the day will not be a sunny day.
So, it is clear that we need to find the value of $P(\overline X )$ .
Now, we know that $P(X) = 0.97$ , so on substituting the value of $P\left( X \right)$ in the equation (1), we will get the required probability.
$\therefore 0.97 + P(\overline X ) = 1 \\\ \therefore P(\overline X ) = 1 - 0.97 \\\ \therefore P(\overline X ) = 0.03 \\\$

Thus, the probability that the day tomorrow will not be a sunny day is 0.03.

Note:
While applying the formula $P(X) + P(\overline X ) = 1$ , we have to be sure that the given events are not inclusive events.
Inclusive events: The events which can happen at the same time are called inclusive events.
Here, a day can either be a sunny day or not a sunny day, but a day cannot be both at the same time. So, the given events are not inclusive events.