Question

From a pack of 52 playing cards Jacks, queens, kings and aces of red color are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is
(i)A black queen
(ii)A red card
(iii)A black jack
(iv)a picture card (Jacks. queens and kings are picture cards)

Answer 1

Answer:

Since jack's ,queen's ,kings and aces are removed.

=> Total outcomes=44

1) a black queen

favourable outcomes = 2

therefore, P(a black queen)= 2/44= 1/22

2)a red colour

favourable outcomes=15

therefore,P(a red card)= 15/44

3)a black jack

favourable outcomes=2

P(a black jack)=2/44=1/22

4)a picture card

favourable outcomes=6

P(a picture card)=6/44=3/22

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Answer 2

SOLUTION :  

Given : Total number of cards in one Deck of cards = 52

King, queen, ace and the Jack of red colour are removed from the pack of 52 playing cards.

Number of remaining cards in one deck = 52 - 8 = 44

Total number of outcomes = 44

(i) Let E1 = Event  of getting a black queen  

Number of black queen in one Deck of cards = 2

Number of outcome favourable to E1 = 2

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

P(E1) = 2/44 = 1/22

Hence, the required probability of getting a black queen , P(E1) = 1/22 .

(ii) Let E2 = Event  of getting a red card  

Number of red card in one Deck of cards = 13 × 2 = 26

King, queen, ace and the Jack of red colour are removed from the pack of 52 playing cards.

Number of red cards removed = 8  

Number of the remaining red cards = 26 - 8 = 18  

Number of outcome favourable to E2 = 18

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

P(E2) = 18/44 = 9/22

Hence, the required probability of getting a red card , P(E2) = 9/22 .

(iii) Let E3 = Event  of getting a black jack

Number of black jack in one Deck of cards = 2

Number of outcome favourable to E3 = 2

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

P(E3) = 2/44 = 1/22

Hence, the required probability of getting a black jack , P(E3) = 1/22 .

(iv) Let E4 = Event  of getting a picture card

Number of picture card in one Deck of cards = 12

[King, queen ,and jack are called face cards. Total number of picture(face) cards are 12.]

King, queen, ace and the Jack of red colour are removed from the pack of 52 playing cards.

Number of picture cards removed of red colour = 6

Number of the remaining picture cards = 12 - 6 = 6  

Number of outcome favourable to E4 = 6

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

P(E4) = 6/44 = 3/22

Hence, the required probability of getting a picture cards , P(E4) = 3/22 .

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