Question

(A) From a pack of 52 playing cards jacks, queens, kings and aces of red colour 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 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 1

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 = ${\displaystyle \frac{2}{44}}={\displaystyle \frac{1}{22}}$
(ii) No. of red cards = 26 – 8 = 18
probability = ${\displaystyle \frac{18}{44}}$ $={\displaystyle \frac{9}{22}}$
(iii) no. of tens = 4
probability = ${\displaystyle \frac{4}{44}}={\displaystyle \frac{1}{11}}$
(iv) No. of remaining picture cards = 2 + 2 + 2 = 6
probability =${\displaystyle \frac{6}{44}}={\displaystyle \frac{3}{22}}$
(B) Total cards = 52 - 12
(i) No. of remaining face cards (only
Kings are remaining) = 4
probability = ${\displaystyle \frac{4}{40}}={\displaystyle \frac{1}{10}}$
(ii) No. of cards that are not face cards = 36
probability = ${\displaystyle \frac{36}{40}}={\displaystyle \frac{9}{10}}$
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 .