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 black jack
(iv) a picture card (Jacks, queens and kings are picture cards).
Answers
Since, Jack's, King, queen and Ace's of red are removed from Deck of cards.
Therefore total no. of playing cards = (52-8)
= 44
(I). P(getting a black queen) = 2 or, 1
44 22
(ii). P(getting a red card) = 18 or, 9
44 22
(III). P(getting a black jack) = 2 or, 1
44 22
(iv). P(getting a picture card ) = 6 or, 3
44 22
Answer:
Total number of outcomes = 52
Cards removed = 2+2+2+2 = 8[2 jack, 2 queen, 2 king and 2 aces of red colour]
Remaining number of cards = 52 – 8=44
Total number of outcomes = 44
(i) Favourable outcomes = 2 [There are 2 black queen]
Required probability =
(ii) Favourable outcomes = number of red cards left = 26 – 8=18
Probability for a red card =
(iii) Favourable outcomes = Number of black jacks = 2
Required probability =
(iv) Number of picture cards left =2+2+2 = 6 [jack, queen, King are picture cards]
Required probability =
(v) Honorable cards [ace, jack, queen and king]
No. of honorable cards left = 2+2+2+2=8
Required probability =