Question

From a pack of 52 cards, all the multiples of 3 are removed. A card is now drawn at random. What is the probability that it is a

(i) a face card ( King , Queen ,Jack)

(ii) an even number red card

• A. 0.3 , 0.5
• B. 0.4 , 0.5
• C. 0.3 , 0.25
• D. 0.5 , 0.4

Answer 1

The correct option is C

0.3 , 0.25

Total number of cards = 52

Number of cards which are multiples of 3 in each suit are 3, 6 and 9.

$\therefore$ Total number of cards which are multiples of 3 = 12 [Since, there are 4 suits].

So, number of cards left = 52 - 12
= 40

(i) Total number of face cards = 12 ( Number of favourable outcomes)

Number of possible outcomes = 40

$\therefore$ Probability to get a face card = $\frac{12}{40}$

= $\frac{3}{10}$
= 0.3

(ii) Even numbered red colored card are 2 , 4 , 6 , 8, 10 ( There are total of 2 red suits )

Hence, there are 10 even numbered of red colored cards Number of possible outcomes = 40

Hence, P( Even numbered red colored card) = $\frac{10}{40}$
= $\frac{1}{4}$
= 0.25