Question

Subject Maths Q1 A card is chosen at random from a deck of 52 cards. Find the probability if it is (a) A King (b) A face card (c) A red card and face card​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf A \: card \: is \: chosen \: at \: random \: from \: a \: deck \: of \: 52 \: cards.$

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

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

$\implies \bf (a) \: \sf A \: King$

$\implies \bf (b) \: \sf A \: face \: card$

$\implies \bf (c) \: \sf Red \: card \: and \: face \: card$

$\bf \underline{ \underline{\maltese\:Solution} }$

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

$\bf \underline{Now},$

$\implies \bf (a) \: \sf A \: King$

$\sf Total \: number \: of \: kings = 4$

$\sf \implies So, number \: of \: favourable \: outcomes = 4$

$\sf Total \: outcomes \: (all \: cards) = 52$

$\sf Hence, probability \: of \: a \: king \: is \: \cancel\dfrac{4}{52} = \bf \dfrac{1}{13}$

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$\implies \bf (b) \: \sf A \: face \: card$

$\sf Total \: number \: of \: face \: card = 12$

$\sf \implies So, number \: of \: favourable \: outcomes =12$

$\sf Total \: outcomes \: (all \: cards) = 52$

$\sf Hence, probability \: of \: a \: face \: card \: is \: \cancel\dfrac{12}{52} = \bf \dfrac{3}{13}$

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$\implies \bf (c) \: \sf Red \: card \: and \: face \: card$

$\sf Total \: number \: of \: face \: card \: from \: both \: the \: red \: suits = 6$

$\sf \implies So, number \: of \: favourable \: outcomes =6$

$\sf Total \: outcomes \: (all \: cards) = 52$

$\sf Hence, probability \: of \: a \: red\: face \: card \: is \:\cancel\dfrac{6}{52} = \bf \dfrac{3}{26}$