Question

The king, queen, jack of clubs is removed from a deck of 52 playing cards and the remaining cards are shuffled. a card is drawn from the remaining cards. Find the probability of getting a card of queen​.

Who will give correct and Explanative Answer I will mark he/she 's ANSWER as brainliest. ​

Answer 1

$\:\;\frak{ \maltese \: \: Given} \: \begin{cases} \star \: \: \sf \underline{Total \: number \: of \: playing \: cards \: in \: the \: deck \: : \longrightarrow \: \bf 52 \: playing \: cards.} \: \: \bigstar \\\star \: \: { \textsf{\textbf {\underline{The \: king, \: queen, \: jack \: of \: clubs \: are \: removed \: from \: the \: deck \: and \: remaining \: cards \: are \: shuffled.}}}} \: \: \bigstar \\ \star \: \:{ \sf{\underline{ \:Number \: of \: card \: is \: drawn \: from \: the \: remaining \: cards \: : \longrightarrow\: \bf A_{(1) }}}} \: \: \bigstar\end{cases}$

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❍ Need To Find :

• The Probability of getting a card of queen.

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$\begin{gathered} \\ \end{gathered}$

❍ Let,

• $\bf{P_{(E)}}$ ➠ Probability of getting an event.
• F ➠ Favourable Outcomes.
• T ➠ Total outcomes.

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$\begin{gathered} \\ \end{gathered}$

★ Key Concept :

• Here, the key concept used in solving this question is the (knowledge of probability of occurance of an event).

Let's do it !!

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✰$\\ \:\: \begin{gathered} \large \: \: \large \underline \frak{Formula \: Used \: : } \\ \end{gathered}$

$\bullet \: \: \: \: {{\textsf{\textbf{Probability \: of \: getting \: an \: event }}}}\: = \: \frac{{ \textsf{ \textbf{Favourable \: outcomes}}}}{{ \textsf{ \textbf{Total \: outcomes}}}}$

$: \longrightarrow\: \: \: \: \underline{ \boxed{\bf{P_{E} \: = \: \frac{F}{T} }}} \: \: \bigstar$

⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀

$\begin{gathered} \large\maltese \: \: \Large \underline \frak{ Solution \: : } \\ \\ \end{gathered}$

$\dag \: \: \frak{ \: \underline {Firstly, \: finding \: the \:{ \textsf{ \textbf{ Favourable \:Outcomes \: }}_{ \sf(F)}} : }}$

➠ No. of queens in the playing cards = 1.

Here, queen of club is removed , Then,

➠ No. of queens left = 4 - 1 = 3.

.°. Favourable Outcomes ➠ 3.

✰❍ ⠀━━━━━━━━━━━━━━━━━━⠀❍ ✰⠀

$\\ \dag \: \: \frak{ \: \underline {Secondly, \: finding \: the \:{ \textsf{ \textbf{Total \: Outcomes }}_{ \sf(T)}} : }}$

➠ No. of playing cards in the deck = 52 playing cards.

Here, king, queen and jack of clubs are removed , Then,

➠ Total Outcomes = 52 - (1 + 1 + 1) = 49

.°. Total Outcomes ➠ 49.

✰❍ ⠀━━━━━━━━━━━━━━━━━━⠀❍ ✰⠀⠀

$\\ \begin{gathered} \dag\: \: \frak{ \: \underline {Substituting \: the \: values \: according \: to \: the \:given \: info \: : }} \\ \end{gathered} </p><p>$

$: \implies {\sf{P_{(E)} \: = \: \frac{F}{T} }} \\\\\ \underline{ \underline{ \boxed {\bf{: \longrightarrow \: P_{(E)} \: = \: \frac{3}{49} }} }} \: \: \bigstar$

$\begin{gathered} {\therefore \: \underline{\boldsymbol{ Hence, } {\rm\: the \: } { \textsf{\textbf { probability \: of \: getting \: a \: card \: of \: queen } }}{ \rm{ \: is \: }}{\bf\: \frac{3}{49} .}}} \\ \\ \end{gathered}$

⠀✰⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀✰⠀

✰ Kindly, slide left ☛ or ☜ right to see full Explanation. ✰

Answer 2

Answer:

\begin{gathered} \:\;\frak{ \maltese \: \: Given} \: \begin{cases} \star \: \: \sf \underline{Total \: number \: of \: playing \: cards \: in \: the \: deck \: : \longrightarrow \: \bf 52 \: playing \: cards.} \: \: \bigstar \\\star \: \: { \textsf{\textbf {\underline{The \: king, \: queen, \: jack \: of \: clubs \: are \: removed \: from \: the \: deck \: and \: remaining \: cards \: are \: shuffled.}}}} \: \: \bigstar \\ \star \: \:{ \sf{\underline{ \:Number \: of \: card \: is \: drawn \: from \: the \: remaining \: cards \: : \longrightarrow\: \bf A_{(1) }}}} \: \: \bigstar\end{cases} \end{gathered}

✠Given

⎩

⎪

⎪

⎨

⎪

⎪

⎧

⋆

Totalnumberofplayingcardsinthedeck:⟶52playingcards.

★

⋆

The king, queen, jack of clubs are removed from the deck and remaining cards are shuffled.

★

⋆

Numberofcardisdrawnfromtheremainingcards:⟶A

(1)

★

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\begin{gathered} \\ \end{gathered}

❍ Need To Find :

The Probability of getting a card of queen.

⠀⠀⠀ ━━━━━━━━━━━━━━━━━━⠀⠀⠀

\begin{gathered}\begin{gathered} \\ \end{gathered} \end{gathered}

❍ Let,

\bf{P_{(E)}}P

(E)

➠ Probability of getting an event.

F ➠ Favourable Outcomes.

T ➠ Total outcomes.

⠀⠀⠀ ━━━━━━━━━━━━━━━━━━⠀⠀⠀

\begin{gathered}\begin{gathered} \\ \end{gathered} \end{gathered}

★ Key Concept :

Here, the key concept used in solving this question is the (knowledge of probability of occurance of an event).

Let's do it !!

⠀⠀⠀ ━━━━━━━━━━━━━━━━━━⠀⠀⠀

✰\begin{gathered}\\ \:\: \begin{gathered} \large \: \: \large \underline \frak{Formula \: Used \: : } \\ \end{gathered} \end{gathered}

FormulaUsed:

\begin{gathered}\bullet \: \: \: \: {{\textsf{\textbf{Probability \: of \: getting \: an \: event }}}}\: = \: \frac{{ \textsf{ \textbf{Favourable \: outcomes}}}}{{ \textsf{ \textbf{Total \: outcomes}}}} \\\end{gathered}

∙Probability of getting an event =

Total outcomes

Favourable outcomes

: \longrightarrow\: \: \: \: \underline{ \boxed{\bf{P_{E} \: = \: \frac{F}{T} }}} \: \: \bigstar:⟶

P

E

=

T

F

★

⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀

\begin{gathered} \\ \end{gathered}

\begin{gathered}\begin{gathered} \large\maltese \: \: \Large \underline \frak{ Solution \: : } \\ \\ \end{gathered} \end{gathered}

✠

Solution:

\begin{gathered} \dag \: \: \frak{ \: \underline {Firstly, \: finding \: the \:{ \textsf{ \textbf{ Favourable \:Outcomes \: }}_{ \sf(F)}} : }} \\ \end{gathered}

†

Firstly,findingthe Favourable Outcomes

(F)

:

➠ No. of queens in the playing cards = 1.

Here, queen of club is removed , Then,

➠ No. of queens left = 4 - 1 = 3.

.°. Favourable Outcomes ➠ 3.

✰❍ ⠀━━━━━━━━━━━━━━━━━━⠀❍ ✰⠀

\begin{gathered} \\ \dag \: \: \frak{ \: \underline {Secondly, \: finding \: the \:{ \textsf{ \textbf{Total \: Outcomes }}_{ \sf(T)}} : }} \\ \end{gathered}

†

Secondly,findingthe Total Outcomes

(T)

:

➠ No. of playing cards in the deck = 52 playing cards.

Here, king, queen and jack of clubs are removed , Then,

➠ Total Outcomes = 52 - (1 + 1 + 1) = 49

.°. Total Outcomes ➠ 49.

✰❍ ⠀━━━━━━━━━━━━━━━━━━⠀❍ ✰⠀⠀

\begin{gathered} \\ \begin{gathered} \dag\: \: \frak{ \: \underline {Substituting \: the \: values \: according \: to \: the \:given \: info \: : }} \\ \end{gathered} < /p > < p > \end{gathered}

†

Substitutingthevaluesaccordingtothegiveninfo:

</p><p>

\begin{gathered} : \implies {\sf{P_{(E)} \: = \: \frac{F}{T} }} \\\\\ \underline{ \underline{ \boxed {\bf{: \longrightarrow \: P_{(E)} \: = \: \frac{3}{49} }} }} \: \: \bigstar\end{gathered}

:⟹P

(E)

=

T

F

:⟶P

(E)

=

49

3

★

\begin{gathered}\begin{gathered} {\therefore \: \underline{\boldsymbol{ Hence, } {\rm\: the \: } { \textsf{\textbf { probability \: of \: getting \: a \: card \: of \: queen } }}{ \rm{ \: is \: }}{\bf\: \frac{3}{49} .}}} \\ \\ \end{gathered} \end{gathered}

∴

Hence,the probability of getting a card of queen is

49

3

.

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✰ Kindly, slide left ☛ or ☜ right to see full Explanation. ✰