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# What is a generalised formula for the probability of mutually exclusive events?

2 years ago

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12 Replies

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A

Antwan Ledner

12 Answers

Shamim H
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Probability of (A Intersection B) = Probability of (A) ADD Probability of (B)

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Kalyani Pujara

P(A or B) = P(A) + P(B) [NOTE: the symbol for the word 'or' in Maths is U, standing for Union. This means it can also be written as 'P(A U B) = P(A) + P(B)']

I

Ibrahim Qayyum

P(A u B) = P(A) + P(B) - P(A n B)

L

Louise Frankland

A

Ayesha Ahmed

A (Intersection) B = {} or empty set(0)

P(A or B) = P(A) + P(B)

Manjit D
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Mutually exclusive events are events that can not happen at the same time eg) you can't get a head and a tail when you toss a coin. When displayed on a venn diagram mutually exclusive events will not have an intersection and so

P(AuB) = P(A) + P(B)

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Paul G
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Mutually exclusive events cannot happen at the same time. If the events are A and B then P(A∩B) = 0.

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J

Jess Xu

**P (A or B) = P (A) + P (B)**

Patric B
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The probability of two events that are mutually exclusive both occurring is simply the product of the individual events happening. This can also be expressed as

P(A & B) = P(A)*P(B)

This does not hold if A and B are not independent, in which case we need to take into account what happens to an event probability given the other event has caused it to changed.** **Let's say that we want to work out the probability of event A & B given under these circumstances.

P(A & B) = P(A)*P(B|A)

Notice the last term in the multiplication has changed. It basically means "Probability of B happening given A has already happened." Note that tree diagrams help a lot with this kinds of thinking!

However for **mutually exclusive events, **the first formula is the one you want!

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J

Joseph

The probability (P) of either event A or event B occurring, when the events are mutually exclusive, is calculated by adding their individual probabilities. Both events cannot occur at the same time hence their probabilities are not related to one another:

P(A or B)=P(A)+P(B)

T

Toluwalope Oluwusi

Akshay K
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If two events A and B are mutually exclusive events, they have no common outcomes hence P(A intersection B) = 0

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