From a pack of 52 playing cards Jacks, queens, kings and aces of red c

1.	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)
Answer» 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

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)

Answer»

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