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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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1616 views

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Antwan Ledner

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

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K
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)']

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Ibrahim Qayyum

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

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Louise Frankland

# P(AUB)=P(A)+P(B)

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Ayesha Ahmed

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

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

Manjit D Verified Sherpa Tutor ✓

Experienced GCSE and A level Maths teacher with 500 hours online

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 Verified Sherpa Tutor ✓

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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 Verified Sherpa Tutor ✓

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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)

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Toluwalope Oluwusi

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

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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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