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Probability Practical

The document outlines the concepts of probability, specifically the addition and multiplication rules, which are essential for solving problems involving multiple events. The addition rule calculates the probability of at least one event occurring, while the multiplication rule determines the probability of multiple independent events happening together. Examples are provided for both rules, illustrating their application in practical scenarios such as card drawing and dice rolling.

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Sachin Choudhari
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54 views1 page

Probability Practical

The document outlines the concepts of probability, specifically the addition and multiplication rules, which are essential for solving problems involving multiple events. The addition rule calculates the probability of at least one event occurring, while the multiplication rule determines the probability of multiple independent events happening together. Examples are provided for both rules, illustrating their application in practical scenarios such as card drawing and dice rolling.

Uploaded by

Sachin Choudhari
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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M. Sc.

Semester IV
PLANT BREEDING AND BIOSTATISTICS Practical II

AIM: To learn concept of Probability (Addition and Multiplication rule)

THEORY: Probability is an important concept for all type of study variable. Theory of
probability deals with several type of problems. To settle problems, there are many rules
related to probability theory. Addition and multiplication rules are one of them. The addition
and multiplication rule are applied to solve the probability problem which has two or more
events.

Addition rule is used to detect probability of one of the two or more events occurring in the
respective random experiment at one task. i.e. at least one event occurred among all events.

Multiplication rule is used to detect outcome that occurs from more than one task in
respective random experiment.

Let us suppose, if there is only one task of tossing a coin two times and find the probability of
getting heads on both time. This type of probability is problem solved by addition rule of the
probability.

Suppose tossing a coin two times one after another. If one get heads on the first toss and also
on the second toss. These two outcomes are independent as outcome of first toss is not
affecting the outcome of second toss. This type of probability problem is solved by
multiplication rule of the probability.

Addition Rule:
Formula: P(A or B) = P(A) + P(B) - P(A and B)
Explanation: To find the probability of either event A or event B happening, add the
individual probabilities of each event, then subtract the probability of both events occurring
simultaneously.
Example (mutually exclusive events):
Scenario: Drawing a card from a standard deck, what's the probability of drawing a heart or a
spade?
Calculation: P(heart or spade) = P(heart) + P(spade) = (13/52) + (13/52) = 1/2

Multiplication Rule:
Formula: P(A and B) = P(A) * P(B/A)
Explanation: To find the probability of both event A and event B happening, multiply the
probability of event A occurring by the probability of event B occurring given that event A
already happened.

Key points about the multiplication rule:


Independent events: If events A and B are independent (one event doesn't affect the
probability of the other), then P(B|A) = P(B), and the formula becomes P(A and B) = P(A)
P(B).
Example (independent events):
 Scenario: Rolling a dice twice, what is the probability of getting a 6 on the first roll and a 3
on the second roll?

 Calculation: P(6 then 3) = P(6) * P(3) = (1/6) * (1/6) = 1/36

Botany Department, Anand Niketan College, Anandwan, Warora Page 1

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