Question

A radio státlon réports news and weather
every 20 minutes for 4 minutes, if the
radlo is turned on at a random time, what
is the probabllty that the news
and weather report is NOT on?
E 0.2
H 0.6
G 0.4
J 0.8

Answer 1

$\huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }$

$\large\underline{ \boxed{ \sf{✰\:Note }}}$

• ➣ Timing of ràdiò station reporting news and weather is every in 20 minutes for 4 minutes
• ➣ Probability :- An event that is likely to occur also A number, between 0 and 1, expressing the precise likelihood of an event happening.
• ➣Denoted by :- P(A)

$\rule{70mm}{2.9pt}$

★ To find ★

• ➣ we have to find Probability when news and weather report is not on
• ➣ we know that Probability

${ \boxed{✠ \: \underline{ \boxed{ \sf{\: P(A) = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: favourable \: outcomes} }}} \: ✠}}$

$\rule{70mm}{2.9pt}$

✛ Here ✛

• ➣ Number of favourable outcomes = 4 min
• ➣ Total number of favourable outcomes = 20 min
• ➣ and P(A) = x

★ Now let's solve according to formula ★

$\qquad \sf \:➛ \: x = \frac {4 }{20} \\ \qquad \sf \:➛ \: x = \frac { \cancel4 }{ \cancel{20}} \\ \qquad \sf \:➛ \: x = 0.2min$

$\rule{70mm}{2.9pt}$

★ Hence probabllty that the news and weather report is NOT on P(A)

$\qquad \qquad{ \boxed{✟\: \underline{ \boxed{ \sf{\:0.2min\green ✓ }}} \:✟ }}$

$\rule{70mm}{2.9pt}$

Hope it helps !