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Lesson

Title: Addition theorem for mutually exclusive events

Grade: 9-a Lesson: S3-L5

Explanation: Hello students, let us learn a new topic in statistics today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Addition theorem for mutually exclusive events:

Addition theorem of probability is known as Theorem of probability.
The Addition theorem of probability states that if A nd B are two mutually exclusive events,then the probability of occurence of either A or B is the sum of the individual probabilities of A and B.

i.e, P (A ∪ B) = P(A) + P(B)

Mutually exclusive Events:

Two events associated with a random experiment are said to be mutually exclusive if both cannot occur together in the same trial or cannot occur together at same time.

$1$

Explanation:

Let \$n\$ be the total number of exhaustic and equally likely cases of an experiment.
Let \$m_1\$ be the number of favourable cases to the happening of the event A

⇒ P(A) = \$m_1/n\$

Let \$m_2\$ be the number of favourable cases to the happening of the event B

⇒ P(B) = \$m_2/n\$

Since,the events A and B are mutually exclusive,the total number of ways in which event A or B can happen is \$m_1 + m_2\$

P (A ∪ B) = \$(m_1 + m_2)/n\$

P (A ∪ B) = \$m_1/n\$ + \$m_2/n\$

P (A ∪ B) = P(A) + P(B)