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One Card is drawn from 52 52 playing cards. What is the probability that the card will be a RED CARD or KING ?

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30 52 \frac{30}{52} 17 52 \frac{17}{52} 7 13 \frac{7}{13} 29 52 \frac{29}{52}

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4 solutions

Sagnik Ghosh
Feb 7, 2015

L e t P ( A ) b e t h e p r o b a b i l i t y o f g e t t i n g r e d c a r d s o u t o f t h e d e c k , L e t P ( B ) b e t h e p r o b a b i l i t y o f g e t t i n g k i n g s o u t o f t h e d e c k a n d L e t P ( A + B ) b e t h e p r o b a b i l i t y o f g e t t i n g a k i n g o r r e d c a r d P ( A ) = 26 52 P ( A B ) = P ( A ) . P ( B ) P ( A B ) = 2 52 P ( B ) = 4 52 P ( A + B ) = P ( A ) + P ( B ) P ( A B ) = 26 52 + 4 52 2 52 = 26 + 4 2 52 = 28 52 P ( A + B ) = 7 13 [ A n s w e r ] Let\quad P(A)\quad be\quad the\quad probability\quad of\quad getting\quad red\quad cards\quad out\quad of\quad the\quad deck\quad ,\\ Let\quad P(B)\quad be\quad the\quad probability\quad of\quad getting\quad kings\quad out\quad of\quad the\quad deck\\ and\quad Let\quad P(A+B)\quad be\quad the\quad probability\quad of\quad getting\quad a\quad king\quad or\quad red\quad card\\ \\ P(A)\quad =\quad \frac { 26 }{ 52 } \quad \\ \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad \quad \quad \quad \quad \quad P(A\quad \cap \quad B)\quad =\quad P(A)\quad .\quad P(B)\\ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad \therefore \quad P(A\quad \cap \quad B)\quad =\quad \frac { 2 }{ 52 } \\ P(B)\quad =\quad \frac { 4 }{ 52 } \\ \\ P(A+B)\quad =\quad P(A)\quad +\quad P(B)\quad -\quad P(A\quad \cap \quad B)\\ \qquad \qquad \quad =\quad \frac { 26 }{ 52 } \quad +\quad \frac { 4 }{ 52 } \quad -\quad \frac { 2 }{ 52 } \\ \qquad \qquad \quad =\quad \frac { 26\quad +\quad 4\quad -\quad 2 }{ 52 } \\ \qquad \qquad \quad =\quad \frac { 28 }{ 52 } \\ \therefore \quad P(A+B)\quad =\quad \frac { 7 }{ 13 } \quad [Answer]\\

Paola Ramírez
Jan 6, 2015

Event ( A ) (A) Red card = 26 =26

Event ( B ) (B) King cards = 4 =4

( A B ) = 2 (A \cup B)=2

P ( A B ) = 26 + 4 2 52 = 28 52 = 7 13 P(A \cup B)=\dfrac{26+4-2}{52}=\dfrac{28}{52}=\boxed{\frac{7}{13}}

You may want to use \dfrac{..}{..} to get bigger fractions. See I have edited your solution.

Pranjal Jain - 6 years, 4 months ago
Abhijeet Parkhi
Dec 17, 2014

out of 52 cards there are 26 cards of red color i.e. probability is 26/52 out of 52 cards there are 4 cards of kings i.e. probability is 4/52 now there are 2 king cards which are red in color i.e.probability is 2/52 ACCORDING TO ADDITION THEOREM P(A OR B)==P(A) +P(B) - P(A AND B) i.e. =====26/52 + 4/52 - 2/52 == 28/52==7/13

Matteo Becchi
Oct 2, 2014

Red cards are 26. Kings that aren't Red are two. So the probability we are looking for is 28/56=7/13.

*28/52 not 28/56

Jack Dunn - 6 years, 8 months ago

I think the question should be RED CARD or RED KING.

Tuan Lo - 6 years, 7 months ago

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Then there wouldn't be a point in asking the question because red kings are red cards, so it would just be one half as probability.

tytan le nguyen - 6 years, 6 months ago

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