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Find the probability that the card drawn is

(i) a black queen (ii) a red card (iii) a ten

(iv) a picture card ( jacks, queen and kings are picture cards ) .

(B) All cards of ace, jack and queen are removed from a deck of playing cards. One card is drawn at random from the remaining cards. Find the probability that the card drawn is

(i) A face card

(ii) Not a face card

Answer

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Hint: In this question the experimental probability has to be calculated keeping in mind the situation given which is removal of jacks, queens, kings and aces of red colour . The probability formula is defined as the possibility of an event to happen , it is equal to the ratio of the number of outcomes and the total number of outcomes.

Complete step-by-step answer:

(A) Total cards = 52 – 8 = 44

(i) No. of queens of black colour = 2

probability = $\dfrac{2}{{44}} = \dfrac{1}{{22}}$

(ii) No. of red cards = 26 – 8 = 18

probability = $\dfrac{{18}}{{44}}$ $ = \dfrac{9}{{22}}$

(iii) no. of tens = 4

probability = $\dfrac{4}{{44}} = \dfrac{1}{{11}}$

(iv) No. of remaining picture cards = 2 + 2 + 2 = 6

probability =$\dfrac{6}{{44}} = \dfrac{3}{{22}}$

(B) Total cards = 52 - 12

(i) No. of remaining face cards (only

Kings are remaining) = 4

probability = $\dfrac{4}{{40}} = \dfrac{1}{{10}}$

(ii) No. of cards that are not face cards = 36

probability = $\dfrac{{36}}{{40}} = \dfrac{9}{{10}}$

Note –

For these kinds of questions your knowledge about a deck of cards plays a vital role in calculating the total number of outcomes as the situation may vary question to question . Remember that jacks , queens and kings are picture cards , face cards or court cards . An ace is not one of them .

Complete step-by-step answer:

(A) Total cards = 52 – 8 = 44

(i) No. of queens of black colour = 2

probability = $\dfrac{2}{{44}} = \dfrac{1}{{22}}$

(ii) No. of red cards = 26 – 8 = 18

probability = $\dfrac{{18}}{{44}}$ $ = \dfrac{9}{{22}}$

(iii) no. of tens = 4

probability = $\dfrac{4}{{44}} = \dfrac{1}{{11}}$

(iv) No. of remaining picture cards = 2 + 2 + 2 = 6

probability =$\dfrac{6}{{44}} = \dfrac{3}{{22}}$

(B) Total cards = 52 - 12

(i) No. of remaining face cards (only

Kings are remaining) = 4

probability = $\dfrac{4}{{40}} = \dfrac{1}{{10}}$

(ii) No. of cards that are not face cards = 36

probability = $\dfrac{{36}}{{40}} = \dfrac{9}{{10}}$

Note –

For these kinds of questions your knowledge about a deck of cards plays a vital role in calculating the total number of outcomes as the situation may vary question to question . Remember that jacks , queens and kings are picture cards , face cards or court cards . An ace is not one of them .