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Q. A card is drawn at random from a well- shuffled pack of 52 cards. Find the probability of getting either a black card or a ace.


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Answer 1

Answer:

$\huge{\boxed{\frac{7}{13}}}$

Step-by-step explanation:

There are 52 cards in all .

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

There are 4 aces , 2 black ones and 2 reds .

$Probability=\frac{Number\:of\:favourable\:outcomes}{Number\:of\: possible\:outcomes}$

Given :

Possible outcomes = 52 .

This includes all the possible outcomes that may arise .

Favourable outcomes include the 4 aces and any black card .

There are 26 black cards and 4 aces .

However 26 black cards already have 2 aces .

Hence we will have more 2 ace which are red .

There are 26 + 2 = 28 favourabale outcomes .

Hence :

$Probability=\frac{28}{52}\\\\\implies \frac{7}{13}$

Answer 2

Question

A card is drawn at random from a well- shuffled pack of 52 cards. Find the probability of getting either a black card or a ace.

Answer

There are total of 52 cards which are well shuffled. It has following contents=>

Four types of card=

Spade, Clubs, Diamond, Heart.

1)Clubs (Black) (13 CARDS)

A,2,3,4,5,6,7 8,9,10,J,Q,K.

2)Spade(Black) (13 CARDS)

A,2,3,4,5,6,7,8,9,10,J,Q,K.

3) DIAMOND(Red) (13 CARDS)

A,2, 3,4,5,6,7,8,9,10,J,Q,K.

4)HEART(RED) (13 Cards)

A,2,3,4,5,6,7,8,9,10,J,Q,K.

THERE ARE FOUR(4) ACES.

(2BLACK ND 2 RED).

THERE ARE 12 FACE CARDS=>

(4 QUEENS,4 JACKS,4 KINGS)





Now, Total black card

=13 Spades + 13 clubs

=26 black cards.

And remaining two ace cards of colour red= 2



So,

getting either a black card or a ace = 2+26=28




Now,

Remember

Probability
=>Number of favourable outcomes/Total number of outcomes





P(Getting a black card or a ace card) = >

Total no. of black card+ red ace cards/Total no.of cards

=>28/52

=>7/13

Hence, probability of getting a black card is 7/13.

Thanks