Question

From a well shuffled pack of cards one card is drawn at random, find
the probability of getting: (a) a queen (b) A black card ​

Answer 1

Answer:

The Total Number of Cards in a Deck = 52

Let The Sample Space Be S

n(S) = 52

There are 26 Black Cards in a Deck

Let the event in which the card drawn is black be B

n(B) = 26

Probability of Getting a Black Cards

= n(B) / n(S)

= 26 / 52

= 1 / 2 ( Dividing Both Numbers by 26 )

Let The Event In Which The Card Drawn Is a Queen be A

The Number of Black Queen in a Deck Is 4

n(A) = 4

Probability of Getting a Queen

= n(A) / n(S)

= 4 / 52

= 1 / 13 ( Dividing Both Numbers by 4 )

The Probability Of Getting a Black Card

= 1 / 2

The Probability of Getting a Queen Card

= 1 / 16

Hope It Helps

Answer 2

Answer:

In a pack of 52 cards, there are 4 queen cards and 13 heart cards.

Let A denote the event that the card drawn is queen and B denote the event that card drawn is heart.

Then,

P(A) = 4/52 and P(B) = 13/52 As there is one card which is both queen and heart (queen of hearts), so P(A and B)= 1/52 Using formula, P(A or B) = P(A) + P(B) – P(A and B) P(A or B) = 4/52 + 13/52 – 1/52 = 16/52 = 4/13

Probability of a card drawn is either a queen or heart = P(A or B) = 4/13