Question

All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is (i) a black face card. (ii) a red card.

Answer 1

Total number of cards in a pack = 52

A pack contains of 4 kings, 4 queens and 4 aces.

∴ Number of cards removed = 4 + 4 + 4 = 12

Remaining number of cards in the pack = 52 − 12 = 40

 

(i) Number of black face cards = 2 (jacks of spade and club)

P(a black face card)=`\text{Number of black face cards}/\text{ Remaining Number of cards in the pack}`

`=2/40`

`=1/20`

Thus, the probability of getting a black face card is`1/20`.

(ii) Remaining number of red cards = 26 − (2 + 2 + 2) = 26 − 6 = 20

P(red card)=`\text{Remaining number of red cards}/\text{Remaining number of  cards in the pack}`

Thus, the probability of getting a red card is`1/2`.