Hey Developer’s, I’m back with a new topic which is Probability of Union Of Events in the series of statistics foundations.

Quick Refresher

A multinomial coefficient is not just of separating two groups of elements but actually separating several groups,more than 2.

{n \choose k_{1},k_{2},\ldots ,k_{m}}={\frac {n!}{k_{1}!\,k_{2}!\cdots k_{m}!}}

So, let’s get started …

Probability of a Union Of Events

We also know that for a set of disjoint events A(i),

P(U A(i)) = Submission

For every two (not necessarily disjoint(Which does not overlap)) events A and B, P(A ⋃ B ) = P(A) + P(B) – P(A ⋂ B)

This can be extended to 3 or more events, Ex: P(A⋃B⋃C) = P(A) +P(B) + P(C) – {P(A ⋂ B) + P(B ⋂ C) + P(A ⋂ C)} + P(P(A ⋂ B ⋂ C))

Example : Consider a cohort of 200 students. 50 students take programming(P),100 students take Electronics(E),150 students take maths (M). 30 Students take programming+electronics,45 students take electronics + maths,25 students take electronics+programming. 15 students take all 3 classes; some students take no classes from the list. What is the probability that a student takes at least one class ?

Solution : P(P) = 50/200, P(E) = 100/200, P(M) = 75/200

P(P ⋂ E) = 30/200, P(E ⋂ M) = 45/200, P(E ⋂ P) = 25/200, P(P ⋂ E ⋂ M) = 15/200

P(P ⋃ E ⋃ M) = 50/200 + 100/200 + 75/200 – {30/200+45/200+25/200}+15/200 = 140/200 = 0.7

Next Post will be on Conditional and Unconditional Probability

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