Question

Out of 100 days the forecast predicted the weather department proved to be true on 20 days chosen any 1 day from these 100 days, the probability that the forecast proved to be false.

Answer 1

Hint: First write all possibilities when a coin is thrown twice. Now count the number of possibilities which are required. Now use the probability formula to get the result you required.
$\text{Probability=}\dfrac{\text{Favoured possibilities}}{\text{Total possibilities}}$

Complete step-by-step solution -
Probability: In a simple way, the probability is how likely something is to happen. Whenever we’re unsure about the outcome of an event we talk about probabilities. It is the value which lies between 0 and 1. Probability is the division result of favorable outcomes, total outcomes.
$\text{Probability=}\dfrac{\text{Favoured possibilities}}{\text{Total possibilities}}$
Given the condition of the event in the question is written as:
If we take 1 random day to check report status
Here, we have 2 possibilities the report forecast may be true or maybe false.
Given total days considered to be as 100 in our case.
Given the number of days, it is true that it is 20.
As the possible outcomes are true and false, we say:
$\left( \text{number of true} \right)+\left( \text{number of false} \right)=\left( \text{total days of report} \right)$ .
By substituting the values, we get the equation as”
$20+\left( \text{number of false} \right)=100$
By simplifying we get the number of false days as:
Number of false $=80$ .
By substituting these into probability formula, we get it as:
Probability of false $=\dfrac{\text{number of false}}{\text{total}}$
By substituting these values, we get:
$P=\dfrac{80}{100}=0.8.$
So, the probability of the report being false is 0.8.

Note: Important point here is to find that true or false is only outcomes possible. There is an alternate method to find the probability of true. Here it is 0.2. Now subtract this form 1 as the possible outcomes are true, false, you can write $\text{false=1-true=1-0}\text{.2=0}\text{.8}$ . Anyways you get the same result.