Mutually Exclusive Events: Overview, Questions, Preparation

An occurrence is an effect or a blend of results of an experiment. Suppose we throw die at you. Let E be the perfect square number case; then the answer is E = {1,4}. Whenever a result follows the criteria given in the scenario, we state that the incident has happened.

It is possible to expand the concept of mutually incompatible events to more than two events as well. More than two occurrences are mutually incompatible if the presence of one of them leaves out the occurrence of all other occurrences. In accordance with the experiment of tossing a single die, events A = {1, 2}, B = {3} and C = {6} are mutually exclusive. We will review what mutually exclusive occurrences of probability are.

Two instances are mutually exclusive or disjoint informal logic if they do not occur simultaneously. Both findings are significant when flipping the coin, which means that at least one of the results must happen since all the options are collectively exhausted by these two possibilities. 

Probability laws are derived from the idea of mutually exclusive events.

Law of Addition: P (A + B) = 1

Law of Subtraction: P (A U B)' = 0

Law of Multiplication: P (A x B) = 0

If the sample space of such an experiment is checked, it is either {H} for the first coin, or {T} for the second coin.

Conditional Probability, for Mutually Exclusive Events:

It is stated as the probability of an event A, provided that another event B has occurred. The conditional probability is denoted by the expression P(B|A) for two independent events B has given A and is defined using the equation:

P(B|A)= P (A ∩ B)/P(A).

Using the multiplication rule to redefine the following equation: P (A ∩ B) = 0

P(B|A)= 0/P(A).

So, for mutually exclusive cases, the conditional probability formula is:

P (A | B) = 0

Probability is an important chapter and carries 10-12 marks in Class 11 exams.

1. What is the probability of a die showing a number 3 or 5?
Solution. Let,
P(3) is the probability of getting a number 3
P(5) is the probability of getting a number 5
P(3) = 1/6 and P(5) = 1/6

So,
P(3 or 5) = P(3) + P(5)
P(3 or 5) = (1/6) + (1/6) = 2/6
P(3 or 5) = ⅓

Therefore, the probability of a die showing 3 or 5 is 1/3.

2. A coin is tossed three times, consider the following events.

Solution.

A: No tail appears
B: Exactly one tail appears
Do they form a set of mutually exclusive events?

The sample space S = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

A = {HHH}

B = { THH, HTH, HHT}

A⋂ B = Ø.

Hence A and B are mutually exclusive events. 

Q: Do mutually exclusive events add up to 1?

Q: How do you solve mutually exclusive problems?

Q: Can two events be dependent and not mutually exclusive?

Q: What is the formula for non-mutually exclusive events?

Q: How do you know if something is mutually exclusive?