Examples based on cards probability

1. Cards Probability

2. Example 1
A card is drawn at random from a well shuffled pack of 52 cards. What is the
probability that the drawn card is king ?
Solution:
The number of outcomes in a deck of cards=52
 n(S) = 52
Let A be the event of drawing a king card.
There are 4 king cards in total.
Then, n(A) = 4
Required probability is
P(A) = n(A) / n(S)
P(A) = 4/52 = 1/13

3. Example 2
A card is drawn at random from a well shuffled pack of 52 cards. What
is the probability that the card is neither a spade nor a Jack ?
Solution:
Let A be the event of drawing a card that is neither spade nor Jack.
There are 13 spade cards in a pack of 52 cards.
(Jack in spade is already included in these 13 cards)
In the remaining 3 types (club, heart, diamond), there are 3 jack cards.

4. Number of spade cards and jack cards is
= 13 + 3
= 16
So, no. of cards which are neither spade nor Jack are
= 52 – 16
= 36
Then, n(A) = 36
n(S) = 52

5. Required probability is
P(A) = n(A) / n(S)
P(A) = 36/52
P(A) = 9/13
So, the required probability is 9/13.

6. Example 3
What is the probability of drawing a black card from a pack of cards?
Solution:
The number of outcomes in a deck of cards=52
 n(S) = 52
Let B be the event of drawing a black card from a pack of cards.
There are 26 black cards in total.
Then, n(B) = 26
Required probability is
P(B) = n(B) / n(S)
P(B) = 26/52 = 1/2