Question

The record of the weather station shows that out of the past 250 consecutive days, it’s wheather forecast were correct 175 times what is the probability of that on a given day was not correct

Answer 1

Given
Total number of weather forecasts=250
Number of weather forecasts which were correct =175
=>Number of incorrect weather forecasts
=250-175
=75
=>P(that on a given day wasn't correct)
=75/250
=3/10

Answer 2

$\huge\fbox\color{lime}{Question༄}$

The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times.

$\huge\fbox\color{lime}{Answer༄}$

i) What is the probability that on a given day it was correct?

⇒ The total number of days for which the record is available = 250 days

⇒ Number of days when forecasts were correct = 175 days

We know the formula of probability

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{Probability = \frac{Number \:of \:favourable \:outcome}{Total \:number \:of \:favourable \:outcome}}}}}}}}}}$

So substitute the value ;

$\bold{P(forecast \:was \:given \:to \:one \:day) = \frac{days \:when \:forecasts \:were \:correct}{Total \:number \:of \:days}}$

$\huge\longrightarrow$ $\bold{\frac{175}{250}}$

$\huge\longrightarrow$ = $\bold{0.7}$

ii) What is the probability that it was not correct on a given day?

⇒ The total number of days for which the record is available = 250 days

⇒ Number of days when forecasts were not correct = 250 - 175 days

So ; ⇒ 75 days

We know the formula of probability

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{Probability = \frac{Number \:of \:favourable \:outcome}{Total \:number \:of \:favourable \:outcome}}}}}}}}}}$

So substitute the value ;

$\bold{P(forecast \:was \:given \:to \:one \:day) = \frac{days \:when \:forecasts \:were \:not \:correct}{Total \:number \:of \:days}}$

$\huge\longrightarrow$ $\bold{\frac{75}{250}}$

$\huge\longrightarrow$ = $\bold{0.3}$

_____________________________________

More information ;

$\bold\red{Probability -}$ The quality or state of being probable; the extent to which something is likely to happen or be the case.

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

${\green{\overline{\green{\underline{\blue{\boxed{\purple{\mathtt{Probability = \frac{Number \:of \:favourable \:outcome}{Total \:number \:of \:favourable \:outcome}}}}}}}}}}$