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# What is a generalised formula for independent events?

3 years ago

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26 Replies

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C

Christiana Schimmel

N
Nina Chopra

P(A and B)= P(A)xP(B)

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P(A and B) = P(A) * P(B)

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M
Mahmudur Rahman

Two events are independent if the probability of happening both of the event at the same time is just the product of the indivial probability of those two events. If you have mulitple events thatare independent then just multiply all of them out. Now there is a catch that some might be dependent and some might not. And things get more interesting when you get into the domain of stochastic processes.

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Yes P(A Intersection B) = P(A) x P(B)

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E
Elisa Bellosta

Events A and B are independent if P(A|B) = P(A). In other words, whether or not B happens has no effect on the probability of A happening. P(A∩B) = P(A) x P(B). That is, the probability of both A and B happening is the product of their individual probabilities

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For two independent events, A and B, P(A|B)=P(A) and P(B|A)=P(B), but also P(A,B)=P(A)P(B). If you can verify that one of these statements is true for two events A and B, then these events are independent and the other statements will also be true.

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Gevik G Verified Sherpa Tutor ✓

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If A and B are two independent events, then the probability of their intersection is equal to the product of the probabilities of each event, that is, P(A n B) = P(A) x P(B)

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William N Verified Sherpa Tutor ✓

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P(A and B) = P(A) * P(B)

P(A and B) means the probability of A and B both occurring is called a compound event

P(A) means the probability of A occurring.

P(B) means the probability of B occurring.

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N
Nicholas Mannan

Independent events are defined as events where their probabilities won't affect each other. Therefore one formula for independent events is P(A and B) = P(A)P(B)

L
Labianta Lekiqi

the generalised formula for independent events for events A and B is

P(A) x P(B)= P(A intersection B)

Intersection symbol looks like n

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There are 2 ways to test for independence

1) P( AnB) = P(A) x P(B)

2) P( A/B) = P(A)

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An event A is said to be independent of another event B if the probability of occurrence of one of them is not affected by the occurrence of the other.

Mathematically, we can say the events A and B are independent if P(A and B) = P(A) x P(B)

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P(A and B) = P(A) x P(B)

where A and B are independent events

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M

P (A and B) = P(A) x P(B)

AND implies to intersection of both said events. If there are more than two events you can add it to the above formula sequentially e.g,

P( A,B and C) = P(A) x P(B) x P(C)

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There are two formulae to be familiar with concerning independence; the one is a consequence of the other.

1. Events A and B are independent if P(A|B) = P(A). In other words, whether or not B happens has no effect on the probability of A happening.
2. P(A∩B) = P(A) x P(B). That is, the probability of both A and B happening is the product of their individual probabilities.

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