PROBABILITY ON CARDS

1. PROBABILITY
Ms. NEHA CHANDRAKANT PATIL
Assistant Professor ( Department of Mathematics)
Changu KanaThakur ACS College( Autonomous) , New Panvel

2. Deck of cards is the term used for a set of
52 cards consisting of different types of
cards.
• There are 4 suits ,13 cards of each suit, consisting
of 1 Ace, 3 face cards, and 9 number cards.
• There are 4 Aces, 12 face cards, and 36 number
cards in a 52 card deck.
• Probability of drawing any card will always lie
between 0 and 1.
• The number of spades, hearts, diamonds, and clubs
is same in every pack of 52 cards.

3. 1)What is the probability of drawing a red card from a
pack of cards?
• Solution:
Here the event E is drawing a red card from a pack of
cards.
The total number of outcomes = 52
The number of red cards (13 of each suit) = 13*2= 26
Hence, the probability of drawing a red card is
P(E) =
26
52
=
1
2

4. 2) Jessica has drawn a card from a well-shuffled
deck. Help her find the probability of the card either
being red or a King.
• Solution:
Jessica knows here that event E is the card drawn
being either red or a King.
The total number of outcomes = 52
There are 26 red cards, and 4 cards which are Kings.
However, 2 of the red cards are Kings.
If we add 26 and 4, we will be counting these two cards
twice.

5. Thus, the correct number of outcomes which are
favorable to E is
26 + 4 - 2 = 28
Hence, the probability of card being red or king is
P(E) =
28
52
=
7
13

6. 3)Determine the probability of the following:
(i)Drawing a Red Queen
(ii)Drawing a King of Spades
(iii)Drawing a Red Number Card
• Solution: let the events E1, E2, and E3 be Drawing a Red
Queen, Drawing a King of Spades, and Drawing a Red Number Card.
The total number of outcomes in every case = 52
(i) Drawing a Red Queen
There are 4 queens in the cards, of which 2 are red and 2 are black.

7. Hence, the probability of event E1 occurring is
P(E1) =
2
52
=
1
13
(ii) Drawing a King of Spades
There are 13 spade cards , of which 1 is King.
Hence, the probability of event E2 occurring is
P(E2) =
1
52

8. (iii)Drawing a Red Number Card
There are 9 number cards in each suit and there
are 2 suits which are red in color.
There are 18 red number cards.
Hence, the probability of event E3 occuring is
P(E3) =
18
52
=
9
26

9. 4) From a shuffled pack of cards, John picks up one
card at random. What is the probability of it being a
hearts' card?
•Solution:
Here the event E is drawing a heart card from a pack
of cards.
The total number of outcomes = 52
The number of heart cards = 13
Hence, the probability of drawing a red card is
P(E) =
13
52
=
1
4

10. 5)From a deck of 52 cards, Justin picks up one at
random. What is the probability of it being a
red non-face card?
• Solution:
Here the event E is drawing a red non-face card from a pack of
cards.
The total number of outcomes = 52
The number of red cards = 13
Number of face cards = 3
Total number of red non-face cards= 13-3 = 10
Hence, the probability of drawing a red non-face card is
P(E) =
10
52
=
5
26