Question

Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is
(i)a king
(ii)of red colour
(iii)a face card
(iv)a queen

Answer 1

★★ A deck of playing cards consists of 52 cards out of which 26 are black cards and  other 26 are red cards, where red cards consists of 13 cards of heart(♥️) ,13 cards of diamond(♦️) and black cards consists of 13 cards  of spades(♠️)and 13 cards are club(♣️).

★★13 cards in each suit are ace,king ,queen, Jack, 10, 9,8,7,6, 5, 4, 3 and 2.

★★ King, queen ,and jack are called face cards.

★★ Total number of face cards are 12.

SOLUTION :  

Given : Total number of cards in one Deck = 52

All red queens and all black jacks are removed from the pack of 52 playing cards.

Number of red queens in one Deck = 2

Number of black jacks in one Deck = 2  

Number of remaining cards in one deck = 52 - (2+2) = 48

Total number of outcomes = 48

(i) Let E1 = Event  of getting a king  

Number of king in one Deck of cards = 4

Number of outcome favourable to E1 = 4

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = 4/48 = 1/12

Hence, the required probability of getting a king , P(E1) = 1/12 .

(ii) Total number of red cards = 26

Two red queens are removed  

Number of red cards left = 26 - 2 = 24

Let E2 = Event  of getting a red card  

Number of outcome favourable to E2 = 24

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 24/48 = 1/2

Hence, the required probability of getting a red card   , P(E2) = 1/2 .

(iii) Total number of face cards = 12

Two red queens and 2 black jacks are removed . Queens and jacks are face cards.

Number of cards removed = 2 + 2 = 4  

Number of face cards left = 12 - 4 = 8

Let E3 = Event  of getting a red card  

Number of outcome favourable to E3 = 8

Probability (E3) = Number of favourable outcomes / Total number of outcomes

P(E3) = 8/48 = 1/6

Hence, the required probability of getting a face card  , P(E3) = 1/6 .

(iv) Let E4 = Event  of getting a queen  

Number of queen in one Deck of cards = 4

Number of queens removed = 2

Number of queens  left = 4 - 2 = 2  

Number of outcome favourable to E4 = 2

Probability (E4) = Number of favourable outcomes / Total number of outcomes

P(E4) = 2/48 = 1/24

Hence, the required probability of getting a queen , P(E4) = 1/24.

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Answer 2

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