Question

A card is drawn from a well-shuffled pack of 52 playing cards. Find the probability that the card drawn is (1) a diamond card (2) a face card (3) a black card.​

Answer 1

Answer:

i) 13/52 = 1/4

ii) 12/52 = 3/13

iii) 26/52 = 1/2

Answer 2

Given,

There are $52$ cards in a well-shuffled pack of playing cards

(1) A diamond card:

We know that, full deck contains $52$ playing cards and there are four different suits in each standard deck-clubs, spades, hearts and diamonds.

So, number of diamond cards in each deck ($52$ cards) $=\frac{52}{4}=13$.

Then, probability of drawing the diamond card $= \frac{13}{52}=\frac{1}{4}$.

(2) A face card:

There are three face cards in each suit i.e., Jack, Queen and king.

Each deck is divided into four suits. So, number of face cards in $52$ playing cards (standard deck) $=3\times4=12$.

Then, probability of drawing the face card $=\frac{12}{52}=\frac{3}{13}$.

(3) A black card;

There are only two colors in the playing cards(Red and black).

So, number of black cards in each deck $=\frac{52}{2} =26$.

Then, probability of drawing the black card $= \frac{26}{52}=\frac{1}{2}$.