## What is a Mutually Exclusive Event?

Mutually Exclusive are those set of events or outcomes that cannot occur at the same time as these events are completely independent, and the outcome of one event does not affect the outcome of another event.

**Example:** Let’s consider a real-life example if you have to be home, but you have an office that day, so both events are mutually exclusive like if you are going to the office, you cannot be at home and vice versa.

When two events can’t happen at the same time, then their probability will also be zero.

**I.e., P (A and B) = 0 (Cannot Happen or Impossible to Happen at Same Time)**

As they are the mutually exclusive events, it will be denoted by **“OR”; it** is also denoted by** the union symbol (U). **as both events cannot happen at the same time, we can find the probability of either or events.

**P (a U b) = P (a) + P (b)**

Where,

- P (a) = Probability of a
- P (b) = Probability of b

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For eg:

Source: Mutually Exclusive (wallstreetmojo.com)

### Explanation of Mutually Exclusive Formula

**Step #1:** If 2 events are mutually exclusive, then find their probability first.

**Step #2: **Once you find the probabilities, the next step is to find their union.

### Examples of Mutually Exclusive Formula

#### Example #1 – For P (a & b ) = 0

**Think you are planning for a tour and you have two choices Italy and Istanbul. If you are calculating the cost, you cannot afford for both the countries. Hence you have to choose one among them. If you want to visit Istanbul, you cannot afford to Italy and vice versa.**

**Here, cost to tour Italy = Rs.2, 00, 000****Cost to Istanbul = Rs.1, 50, 000****And your budget = Rs.2, 20, 000**

**Solution:**

Use the below data for calculation of Mutually Exclusive Event.

Calculation of Mutually Exclusive Event can be done as follows:

Tour cost in Italy & Istanbul = 2, 00,000 + 1, 50,000

**Tour cost in Italy & Istanbul = 3 50 000 (0 mutually exclusive as you can’t visit both at the same time as your budget is 2, 20, 000 only).**

#### Example #2 – For P (A U B) = P (A) +P (B)

**A final handball match is arranged between two teams England and India. The audience is asked to vote on which team will be winning the match, and they voted as below, assume there are 1000 people in the stadium.**

**Solution:**

Use the below data for calculation of Mutually Exclusive Event.

The calculation can be done as follows:

Probability of India winning the match (A) = 650/1000 =0.65

Probability of England winning the match (B) = 150/1000=0.15

Probability of match becoming draw P (A ∩ B) = 0 (as it is finally there won’t be a draw)

P (A U B) = P (A) + P (B)

P (A U B) = 0.65 + 0.15

**P (A U B) = 80%**

#### Example #3 – For P (A U B) = P(A) + P (B)

**Let’s consider this example for choosing between events that mutually exclusive.**

**We have a pack of 52 cards, and you are asked to choose 1 card, which is a joker as well as number 7.****Here you don’t have a card which has number 7 and joker; hence it is proved that P (A and B) = 0.****So, we can either choose a card which has a number 7 or a joker.**

**Solution:**

Use given data for calculation of Mutually exclusive Event.

Calculation of Mutually Exclusive Event can be done as follows:

Then, P (A U B) = P (A) + P (B)

- P (A) = number 7 cards = 4/52=1/13=0.0769
- P (B) = getting a joker = 4/52 = 1/13=0.0769
- P (A U B) = 0.0769 + 0.0769

**P (A U B) = 0. 15385**

### Recommended Articles

This has been a guide to Mutually Exclusive Formula. Here we discuss how to calculate mutually exclusive events using its formula along with examples and a downloadable excel template. You can learn more about financial analysis from the following articles –

- Mutually Exclusive Projects
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- Calculate Joint Probability
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