Question

A card is drawn at random from a pack of 52 cards.
Find the probability that the card drawn is
(i) black
(ii) red and a queen
(ii) neither heart nor a king
(iv) an ace, jack or a king
(v) '10' of diamonds
(vi) club or an ace.

solve it with step wise​

Answer 1

Answer:

i)1/2

ii)29/52

iii)4/13

...

Answer 2

Answer:

i. 1/2

ii. 1/26

iii. 9/13

iv. 3/13

v. 1/52

vi. 4/13

Step-by-step explanation:

There are 52 cards in a pack of card. The card divided into 4 groups Hearts  , Diamonds, Clubs & Hearts. the 'As' are Known as Ace. The 'Ks' are known as King. The 'Qs' are known as Queen. The 'Js' are known as Jack.

The Ace,King,Queen & Jack are known as  Face Cards.

All the face cards are 4 in number.

i. Total number of black cards = 26

  Total number of cards = 52

therefor probability of getting a black card = 26/52

                                                                        = 1/2

ii.   Total numbers of cards that are red and a queen =  2

     Total numbers of cards = 52

     therefor the probability of getting a card that is red and a queen is

                                                                                                                  =  2/52

                                                                                                                    = 1/26

iii. Numbers of cards other than a heart = 52 - 13

                                                                   = 39

   Number of number of cards that are king = 4

   So, total numbers of cards that is neither a hearts or a king = 39 - 3.

                                                                                                        = 36

    [We are taking 3 king card because we have already removed a king              

     card when we deducted the heart cards from the pack.]

   Total numbers of cards are = 52

   Therefor probability of getting a card that is neither a heart or a king is

    = 36/52

    =9/13

iv. Total number of ace cards = 4

    Total number of jack cards = 4

    Total number of king cards = 4

    Total number of cards = 52

    Therefor probability of getting a card that is an ace, jack or a king

    = (4+4+4)/52

    = 12/52

    = 3/13

v.  Number of card that is '10' of diamonds is = 1

   Total numbers of cards =52

   Therefor probability of getting a card that is '10' of diamonds is = 1/52

vi. Numbers of club cards = 13

    Number of ace cards = 4              [Exclude the ace of club while adding

                                                                 the numbers together]

    Total number of cards that is a club or an ace = 13+3

                                                                                 = 16

    Total number of cards = 52

    Therefor the probability of getting a card that is a club or an ace = 16/52

                                                                                                                 = 4/13