Question

One card is draw from a well - shuffled deck of 52 cards. Find the probability of getting either a black card or a king.
​

Answer 1

Total number of cards = 52

so,

$\boxed{RED\:CARD=26}\\ \\ \boxed{BLACK\:CARD=26}\\ \\ \boxed{KINGS=4[BLACK\:2 +RED\:2]}$

Now,

Probability of not getting a black card or a king:-

Number of black cards=26

Number of kings=4-2=2 [as black kings are already included in the black cards]

Total favourable cards = 52-[26+2] =52- 28=24

now,

$\boxed{P[E]=\frac{favourable\:outcomes}{total\:outcomes}}$

so,

$P[not\:getting\:black\:card\:or\:king]= \dfrac{24}{52}=\dfrac{6}{13}$

now we know that

$\boxed{0\leq P\leq 1}$

so,

Probability of getting either a black card or a king is as follows:-

$1-\dfrac{6}{13}= \dfrac{13-6}{13}=\dfrac{7}{13}$

Answer 2

Answer:- 7/13

Step by Step Solution:-

We know  that,

There  are 26  red card  and  26 black cards in a deck of  52 card

Now, There  are  2 cards of  black king  and 2 cards  of  black king.

Calculating favourable cases:-

Number of  black cards = 26

Number  of kings =  4

This  '4' includes 2  red kings  and  2  black kings but  if  we  talk about total number of  black card (26) , it already includes 2 kings

So,

Favourable number of  kings  will be 2 as  we  have  already counted 2 black king while  counting total number of  black card.

Hence,

Total number  of  favourable  cases:- 26 + 2 = 28

Therefore,

Probability of getting either a black card or a king,

= Favourable cases/Total cases

= 28/52

= 14/26

= 7/13