Question

A card is drawn from well shuffled deck of 52 cards randomly what is the probability of getting a card which is neither an ace nor a king card

Answer 1

Answer

11/13

$\rule{200}2$

A card is drawn from a well-shuffled deck of 52 cards randomly.

So,

Total number of outcomes = 52

We have to find the probability of getting a card which is neither an ace nor a king card.

Total number of ace = 4 and Total number of King = 4

Number of favourable outcomes = 52 - (4 + 4) = 52 - 8

= 44

Now,

Probability = $\sf{\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}}$

Substitute the known values

⇒ $\sf{\dfrac{44}{52}}$

On simplifying we get,

⇒ $\sf{\dfrac{11}{13}}$

Answer 2

Answer:

Total number of outcomes = 52

Number of Favourable outcomes = ?

There are 52 cards. 26 are red and 26 are black.

The red cards have 2 kings, one of heart and the other of diamond. Also, the red cards have 2 ace, one from diamond and the other from hearts.

Similarly, the black cards have 2 kings, one of spades and the other of clubs. Also, the red cards have 2 ace, one from spades and the other from clubs.

So, the total number of cards that are ace and king are = 4 + 4 = 8

Hence, the total number of Favourable outcomes = 52 - 8 = 44 cards.

The Formula to find the probability =

$\mapsto\pink{\tt{\dfrac{No.\:of\:Favourable\:o/c}{Total\:no.\:of\:o/c}}}$

$\mapsto\tt{\cancel{\dfrac{44}{52}}}$

$\mapsto\green{\underline{\tt{\dfrac{11}{13}}}}$

$\rule{200}4$