Question

If all even number cards are removed from a pack of 52 cards, what is the probability that a card picked up is :i) A face card.ii) A multiple of 3 of Clubs.iii) Red multiple of 5.iv) A prime numbered cards.

Answer 1

Solution:

There are total 4 suits in the deck of 52 playing cards.

♠️:A,2,3,4,5,6,7,8,9,10,J,Q,K

♥️:A,2,3,4,5,6,7,8,9,10,J,Q,K

♥️ :A,2,3,4,5,6,7,8,9,10,J,Q,K

♣️:A,2,3,4,5,6,7,8,9,10,J,Q,K

According to the question all even numbered cards are removed,ie 2,4,6,8,10 are removed from each suit.
Total cards removed:20

Total cards left in the deck : 32

1) probability of getting a face card:

Total face cards(Favourable outcome)= 12

Total outcome:32

let F is the event of drawing a face card

$p(F) = \frac{12}{32} \\ \\ = \frac{6}{16} \\ \\ p(F) = \frac{3}{8}$

2)A multiple of 3 of Clubs:

Favourable outcome : 3,9
Total outcomes= 32

if C is the event of drawing a card which is
multiple of 3 of clubs, then probability

$p(C) = \frac{2}{32} \\ \\ = \frac{1}{16}$
3) Red multiple of 5:

Favourable outcomes: ♥️5,♥️ 5

if R is the event of drawing a card which is
multiple of 5 of red colour, then probability

$p(R) = \frac{2}{32} \\ \\ = \frac{1}{16}$

4) A prime numbered cards:

Favourable outcome:12
♠️3,5,7
♥️3,5,7
♥️ 3,5,7

♣️3,5,7

if P is the event of drawing a card which is a prime number, then probability

$p(P) = \frac{12}{32} \\ \\ = \frac{3}{8}$

Hope it helps you.