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.
The 4 kings, 4 queens, and 4 aces are removed.
Thus, remaining number of cards = 52 – 4 – 4 – 4 = Total number of elementary event = 40.
(i) Let E be the event of getting a black face card
Number of black face cards = 2 (only black jacks) = number of favourable event
∴ P (getting a black face card) = P (E) = 2/40 = 1/20
(ii) Let E be the event of getting a red card
Number of favourable events = Number of red cards now = 26 – 6 = 20 being total red cards 26 out of which 6 are withdrawn
∴ P (getting a red card) = P (E) = 20/ 40 = 1/2