Question

029. The face cards of red cards are removed from a pack of 52 playing cards. The remaining
cards are well shuffled and then a card is drawn from it. Find the probability that itis
(1) the jeck of aspade (2) a red face cards (3) a king and a queen.
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Answer 1

$\bf \underline{Given} :$

The face cards of red colour are removed from a pack of 52 playing cards. The rest of the cards are well shuffled and then a card is drawn from it.

$\bf \underline{To \: find} :$

$\sf We \: have \: to \: find \: the \: probability \: of :$

$\bf (1). \sf \: The \: jack \: of \: spades$

$\bf(2). \: \sf A \: red \: face \: card$

$\bf(3). \sf \: A \: king \: and \: a \: queen$

$\bf \underline{Formula \: to \: be \: used} ,$

$\boxed{ \pink{ \sf Probability \: of \: an \: event \: (P) = \dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes} }}$

$\bf \underline{\underline{Solution} }$

$\sf \underline{Some \: basic \: informations} :$

$\bf(1). \sf \: Total \: face \: cards = 12$

$\bf(2). \sf \: Total \: red \: color \: face \: cards \: (Hearts \: and \: Diamonds) \:= 6$

$\bf(3). \sf \: Total \: black \: color \: face \: cards \: (Club \: and \: Spades) \: = 6$

$\bf Now,$

$\sf \underline{According \: to \: question},$

$\sf \implies Total \: outcome = 52 - 6 = 46$

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Solution : 1

$\sf Total \: number \: of \: jack \: of \: spades = 1$

$\sf Hence, favourable \: outcome \: is \: 1$

$\sf \: So, answer = \dfrac{1}{46}$

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Solution : 2

Here, in the question it is mentioned that red face cards are removed...

$\sf Therefore, favourable \: outcome = 0$

$\sf \: So, answer = \dfrac{0}{46}$

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Solution : 3

$\sf Total \: number \: of \: king \: and \: queen = 8$

$\sf \underline{But \: according \: to \: question},$

$\sf Total \: favourable \: outcomes = 8 - 4 = 4$

$\sf \: So, answer = \cancel{\dfrac{4}{46} } = \dfrac{2}{23}$

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