Question

A coin is tossed 1000 times with the following frequencies:
Head : 455, Tail : 545
Compute the probability for each event.


$\bold{with \: full \: explanation}$


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Answer 1

$\Huge \underline{\boxed {\bf{Answer:}}}$

$\Large \underline{\underline{\red {\frak{Given::}}}}$

$\sf{ \mapsto{Total \: times \: coins \: tossed=1,000 times}}$

$\sf {\mapsto{Frequency \: of \: head=455 times}}$

$\sf {\mapsto{Frequency \: of \: tail=545 times}}$

$\Large \underline{\underline{\red {\frak{To \: find::}}}}$

$\sf {\leadsto{Compute \: the \: probability \: of \: each \: event.}}$

$\Large \underline{\underline{\red {\frak{Formula \: required::}}}}$

$\pink \star{ \boxed{ \sf{P(E) = \frac{Number \: of \: trials \: in \: which \: the \: event \: happens \: }{Total \: number \: of \: trails} = \frac{m}{n} }}} \pink \star$

$\Large \underline{\underline{\red {\frak{According \: to \: Question::}}}}$

${ \implies{ \sf{P(E) = \frac{Number \: of \: trials \: in \: which \: the \: event \: happens \: }{Total \: number \: of \: trails} = \frac{m}{n} }}}$

${ \implies{ \sf{P(H)= \frac{455}{1,000} = 0.455 }}}$

${\implies{\bf{Probability \: of \: head \: is \: 0.455.}}}$

${ \implies{ \sf{P(E) = \frac{Number \: of \: trials \: in \: which \: the \: event \: happens \: }{Total \: number \: of \: trails} = \frac{m}{n} }}}$

${ \implies{ \sf{P(T)= \frac{545}{1,000} =0.545 }}}$

${\implies{\bf{Probability \: of \: tail \: is \: 0.545.}}}$

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Answer 2

Step-by-step explanation:

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$\Large\bf{\underbrace{\underline{Question:-}}}$

:$\Longrightarrow$ ● A coin is tossed 1000 times with the following frequencies:

Head : 455, Tail : 545 Compute the probability for each event.

$\Large\bf{\underbrace{\underline{To\ find:-}}}$

:$\Longrightarrow$ ● In this question we have to find the probability for each event.

$\Large\bf{\underbrace{\underline{Given:-}}}$

:$\Longrightarrow$ $\sf{●\ Total\ outcomes\ =\ 1000.}$

:$\Longrightarrow$ $\sf{●\ Frequency\ of\ heads\ =\ 455.}$

:$\Longrightarrow$ $\sf{●\ Frequency\ of\ tails\ =\ 545.}$

$\Large\bf{\underbrace{\underline{Solution:-}}}$

:$\Longrightarrow$ ● In this question we are asked to find out the probability of all the possible outcomes. The "two possible outcomes" while tossing a coin are occurrence of heads and occurrence of tails. Therefore, we consider the two probabilities and calculate the result according.

$\bf{\underbrace{\underline{According\ to\ the\ question:-}}}$

:$\Longrightarrow$ $\sf{\qquad Let\ H\ be\ event\ of\ heads\ coming. \qquad}$

:$\Longrightarrow$ $\sf{\qquad And\ T\ be\ event\ of\ tails\ coming. \qquad}$

:$\Longrightarrow$ $\sf{\qquad Probability\ of\ heads\ =\ P(H)\ =\ \bigg (\dfrac{Number\ of\ heads}{Total\ number\ of\ trails} \bigg) \qquad}$

:$\Longrightarrow$ $\sf{\qquad =\ \bigg (\dfrac{455}{1000} \bigg) \qquad}$

:$\Longrightarrow$ $\sf\pink{\qquad =\ 0.455 \qquad}$

$\bf{\underbrace{\underline{Probability\ of\ heads\ =\ 0.455}}}$

:$\Longrightarrow$ $\sf{\qquad Probability\ of\ tails\ =\ P(T)\ =\ \bigg (\dfrac{Number\ of\ tails}{Total\ number\ of\ trails} \bigg) \qquad}$

:$\Longrightarrow$ $\sf{\qquad =\ \bigg (\dfrac{545}{1000} \bigg) \qquad}$

:$\Longrightarrow$ $\sf\pink{\qquad =\ 0.545 \qquad}$

$\bf{\underbrace{\underline{Probabilitiy\ of\ tails\ =\ 0.545}}}$

$\Large\bf{\underbrace{\underline{Hence\ Verified}}}$

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