Question

From a pack of 52 playing cards jack, queen and king of clubs are removed and then well shuffled. From the remaining cards a card is drawn. Find the probability of getting:
i) a face card
ii) a club
iii) a black card
iv) a non face card
v) a king
vi) a red face card
[6 MARKS]

Answer 1

Each subpart: 1 Mark each

Number of cards removed = 3 (face cards of clubs)
Remaining number of cards = 52 - 3 = 49
i) Number of face cards left = 12 - 3 = 9
$\therefore$ P(a face card) $=\frac{9}{49}$

ii) Remaining number of clubs = 13 - 3 = 10
$\therefore$ P(a club) $=\frac{10}{49}$

iii) Remaining number of black cards = 26 - 3 = 23
$\therefore$ P(a black card) $=\frac{23}{49}$

iv) Remaining number of a non face card = 49 - 9 = 40
$\therefore$ P(a non face card) $=\frac{40}{49}$

v) Remaining number of kings = 4 - 1 = 3
$\therefore$ P(a king) $=\frac{3}{49}$

vi) P(a red face card) $=\frac{6}{49}$