Question

All the kings, Queens and jacks are taken out from a deck of 52 playing cards, then one card is drawn from this well shuffled deck. Find the probability that the card drawn is

(i) A black coloured face card

(ii) A red card.

Answer 1

Total number of playing cards in a deck = 52.

The number of face cards 

i.e., kings, queens, jacks = 12

Taking out all face cards the number of remaining cards 

= 52 – 12 = 40.

∴ Total number of all possible outcomes = 40

(i) Number of face cards in the remaining playing cards.

Let the event that the black face card drawn be A = 0.

∴ The probability that the card drawn is a black face card P(A) = \(\frac { 0 }{ 40 }\) = 0

This is an impossible event.

(ii) Let occurring the event that the card drawn be (B).

Red cards in the remaining cards = 20.

∴ The number of favourable outcomes of event (B)

= 20.

∴ P(B) = \(\frac { 20 }{ 40 }\) = \(\frac { 1 }{ 2 }\)

Hence (i) P(A) = 0 (ii) P(B) = \(\frac { 1 }{ 2 }\)