Question

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) Select the correct answer from above options

Answer 1

We know that, Total no. of cards = 52 All jacks, queens & kings, aces of red colour are removed. Total no. of possible outcomes = 52 – 2 – 2 – 2 – 2 = 44 (remaining cards) (i) Let E = event of getting a black queen No. of favourable outcomes = 2 (queen of spade & club) Probability, P(E) = Number of favourable outcomes/ Total number of outcomes P(E) = 1/22 (ii) Let E = event of getting a red card No. of favourable outcomes = 26 – 8 = 18 (total red cards jacks – queens, kings, aces of red colour) Probability, P(E) = Number of favourable outcomes/ Total number of outcomes P(E) = 18/44 = 9/22 (iii) Let E = event of getting a black jack No. of favourable outcomes = 2 (jack of club & spade) Probability, P(E) = Number of favourable outcomes/ Total number of outcomes P(E) = 2/44 = 1/22 (iv) Let E = event of getting a picture card No. of favourable outcomes = 6 (2 jacks, 2 kings & 2 queens of black colour) Probability, P(E) = Number of favourable outcomes/ Total number of outcomes P(E) = 6/44 = 3/22