Question

From a well-shuffled pack of 52 playing cards, one card is drawn at random. What is the probability that the card drawn will be a black king ?

Answer 1

$\mathbb{\underline{\orange{Points\: to\: remember:}}}$

¶¶¶ In a Deck of cards,

• No. of shapes = 4
viz., Hearts, diamonds, spades, clubs

• No. of black cards = 26
• No. of red cards = 26

• No. of Kings = 4

¶¶¶ Probability of Occurrence of Event
$= \frac{No.\: of\: favourable\: outcomes}{No.\: of\: Total\: Outcomes}$

$\mathfrak{\huge{\underline{\blue{Solution:}}}}$

Let S be sample space
n(S) - no. of ways of drawing a card from a deck of 52 cards.
$n(S) = 52_{C}__{1}$

•°• n(S) = 52

Let E be Event that a card drawn from the deck of cards is a black king

E = {King of Spades, King of Clubs}
^^ Only 2 favourable cases for Event E occurrence

n(E) - No. of favourable cases for occurrence of Event
$n(E) = 2_{C}__{1}$

•°• n(E) = 2

$Probability = \frac{n(E)}{n(S)}$

$Probability = \frac{2}{52} = \frac{1}{26}$

•°•
$\underline{\underline{Required\: Probability = \frac{1}{26}}}$

$\mathfrak{\huge{\red{Cheers}}}$

$\mathcal{\huge{\orange{Hope\: it\: Helps}}}$

Answer 2

Total number of all possible outcomes =52

Let E be the event of getting a red card or a king.

There are 26 red cards (including king) and there are 2 more kings,

So,the number of favorable outcomes =(26+2)=28

P(getting a red card or a king )=P(E)=28/52=7/13