Question

$\huge\underbrace\mathfrak\color{lime}{ †\: Question:–}$
The record of a weather station shows that out of the past 250 consecutive
days, its weather forecasts were correct 175 times.

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

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Answer 1

$\huge\fbox\color{lime}{Question༄}$

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.

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

Answer 2

$\huge \colorbox{lime}{question}$

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

$\huge \colorbox{lime}{answer}$

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

${ \red{ \overline{ \green {\ { \blue{ \boxed{ \purple{probability = \{number \: of \: favourable \: outcome}{total \: number \: of \: favourable \: outcome}}}}}}}}$

So substitute the value ;

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

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

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

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

${ \green{ \overline{ \green{ \underline{ \blue{ \boxed{ \orange {probability = {number \: of \: favourable \: outcome}{total \: number \: of \: favourable \: outcome}}}}}}}}}$

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.

${ \red{ \overline{ \green{ \underline{ \purple{ \boxed{ \purple{ \probability = \{number \: of \: favourable \: outcome}{total \: number \: of \: favourable \: outcome}}}}}}}}$