This document contains solutions to probability problems involving drawing cards from a standard 52-card deck. It calculates the probabilities of: 1) Drawing specific cards like the 2 of spades, a jack, a diamond suit card, or a king/queen. 2) Drawing a numbered card (2-10). 3) Drawing the 3 of diamonds specifically. 4) Drawing a non-ace card. All probabilities are calculated as the number of desired outcomes divided by the total number of possible outcomes (52 cards in the deck).

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

2. 1) A card is drawn from a well-shuffled pack of 52 cards. Find the probability of
getting:
(i) ‘2’ of spades
(ii) a jack
(iv) a card of diamond
(v) a king or a queen
Solution:
Total no. of cards = 52
So total no. of possible outcomes, n(S) = 52
(i) Let E1 denotes the event of getting 2 of spades.
No. of ‘2’ of spades = 1
n(E1) = 1

3. P (getting 2 of spades) =
1
52
(ii) Let E2 denotes the event of getting a jack.
No. of jacks in a suit = 4
n(E2) = 4
P (getting a jack) =
4
52
=
1
13

4. Let E4 denotes the event of getting a card of diamond.
No. of diamond cards = 13
n(E4) = 13
P (getting a card of diamond) =
= n(E4)/ n(S)
= 13/52
= 1/4

5. (v) Let E5 denotes the event of getting a king or a queen.
No. of kings and queen = 4+4= 8
n(E5) = 8
P (getting a king or a queen)
= n(E5)/ n(S)
= 8/52
= 2/13

6. 2) Find the probability of getting a numbered card
when a card is drawn from the pack of 52 cards.
Solution : Here the event E is drawing a numbered card from a
pack of cards.
The total number of outcomes = 52
The numbered cards= 2, 3, 4, 5, 6, 7, 8, 9, 10
Since there are 4 suits,
n(E)= 9*4= 36
Hence, the probability of drawing a numbered card is
P(E) =
36
52
=
9
13

7. 3) A card is drawn at random from a deck of cards.
Find the probability of getting the 3 of diamond.
 Solution:
Here the event E is drawing a 3 of diamond from a pack of cards.
The total number of outcomes = 52
There are 13 diamond cards
The number of 3 of diamond = 1
n(E)= 1
Hence, the probability of drawing a numbered card is
P(E) =
1
52

8. 4)A card is drawn from a well shuffled
pack of 52 cards. Find the probability of
a non-ace?
 Solution:
Number of ace cards in each of four suits namely spades, hearts,
diamonds and clubs = 1
Therefore, total number of ace cards out of 52 cards = 4
Thus, total number of non-ace cards out of 52 cards = 52 - 4
= 48
Therefore, probability of getting ‘a non-ace’ card
=
48
52
=
12
13