Question

Rain As the author is creating this exercise, a weather reporter stated that there is a 20% chance of rain tomorrow. What is the probability of no rain tomorrow?

Short answer

The probability of no rain tomorrow is 0.8.

Step-by-step solution

Given information

The chances that it would rain are 20%.

Describe the probability of any event

A value that measures the chances of occurrence of a specific event is termed as the probability corresponding to the event.

For any event E, the probability can be mathematically formulated as:

$P\left(E\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

The value of a defined event always lies between 0 to 1.

Properties of the probability of an event

The probability value can be obtained from the percentage value by dividing it by 100.

The probability of the event and its complement is always 1.

$P\left(E\right)+P\left(\overline{E}\right)=1$

Define the event and compute the probability

Consider event A as the event that it rains tomorrow.

Complementary to this, the event that it does not rain tomorrow is satisfied as the occurrence of rain may or may not occur.

Thus, $\overline{A}$ is defined as the event that there will be no rain tomorrow.

Using the properties, the probability that there will be no rain tomorrow is given as:

$$\begin{gathered} P\left(\overline{A}\right)=1-P\left(A\right) \\ =1-0.20 \\ =0.8 \end{gathered}$$

Thus, the probability of no rain tomorrow is 0.8.