Probability of cards
In a pack or deck of 52 playing cards, they are divided into
4 suits of 13
QUESTION
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(i) ‘2’ of spades (ii) a jack
(iii) a king of red colour. (iv) A card of diamond
(Vi) Neither a queen nor a jack.
(vII) a king or a queen
QUESTION
A card is drawn from a well-shuffled pack of 52 cards. Find the probability
that the card drawn is:
(i) A red face card
Number of face card in hearts = 3, Number of face card in diamonds = 3
Total number of red face card out of 52 cards = 3 + 3 = 6
Therefore, the probability of getting ‘a red face card’ = 6/52
(ii) Neither a club nor a spade
Number of card which is neither a club nor a spade = 52 - 26 = 26,
= 26/52
(iii) Neither an ace nor a king of red color
Number of ace and king of red color = 4 + 2 = 6
Number of card which is neither an ace nor a king of red color = 52 - 6 = 4
Therefore, the probability of getting ‘neither an ace nor a king of red
color’=4/52
(iv) Neither a red card nor a queen
Total number of red card and queen = 13 + 13 + 2 = 28,
Number of card which is neither a red card nor a queen = 52 - 28 = 24
Therefore, the probability of getting ‘neither a red card nor a queen = 24/52
Additive Rules of Probability
Disjoint: Two events that cannot occur at the same time are called disjoint or
mutually exclusive. (We will use disjoint.)
EXAMPLE:
Consider the following two events:
A — a randomly chosen person has blood type A, and
B — a randomly chosen person has blood type B.
In rare cases, it is possible for a person to have more than one type of blood
flowing through his or her veins, but for our purposes, we are going to
assume that each person can have only one blood type. Therefore, it is
impossible for the events A and B to occur together.
Events A and B are DISJOINT
EXAMPLE:
Consider the following two events:
A — a randomly chosen person has blood type A
B — a randomly chosen person is a woman.
In this case, it is possible for events A and B to occur together.
Events A and B are NOT DISJOINT.
The Venn diagrams suggest that another way to think about disjoint versus
not disjoint events is that disjoint events do not overlap. They do not share
any of the possible outcomes, and therefore cannot happen together.
On the other hand, events that are not disjoint are overlapping in the sense
that they share some of the possible outcomes and therefore can occur at the
same time.
Finding P(A or B) for disjoint events.
The Addition Rule for Disjoint Events:
If A and B are disjoint events, then
P(A or B) = P(A) + P(B)
QUESTION
A statistics class for engineers consists of 25 industrial, 10 mechanical, 10
electrical and 8 civil engineering students. If a person is randomly selected
by the instructor to answer a question, find the probability that the student
chosen is (a) an industrial engineering major and (b) a civil engineering or an
electrical engineering major.
QUESTION
What is the probability of getting a total of 7 or 11 when a pair of fair dice is
tossed?
Let's look at some experiments in which the events are non-mutually
exclusive.
Additional Rule 2: When two events, A and B, are non-mutually exclusive,
the probability that A or B will occur is:
P(A or B) = P(A) + P(B) - P(A and B)
In the rule above, P(A and B) refers to the overlap of the two events. Let's
apply this rule to some other experiments.
Experiment: A single card is chosen at random from
a standard deck of 52 playing cards. What is the
probability of choosing a king or a club?
Solution
