Which of the following expressions gives the probability of an event when the sample…

MATHEMATICS · Single correct · CBSE · Mathematics · Probability · Probability

Problem

Which of the following expressions gives the probability of an event AA when the sample space is divided into mutually exclusive and exhaustive events E1,E2,…,EnE_1,E_2,\dots ,E_n? (a) ∑i=1nP(A) P(Ei∣A)\displaystyle \sum_{i=1}^{n} P(A)\,P(E_i\mid A) (b) ∏i=1nP(A∣Ei)\displaystyle \prod_{i=1}^{n} P(A\mid E_i) (c) ∑i=1nP(Ei) P(A∣Ei)\displaystyle \sum_{i=1}^{n} P(E_i)\,P(A\mid E_i) (d) P(A∣E1)+P(A∣E2)+⋯+P(A∣En)\displaystyle P(A\mid E_1)+P(A\mid E_2)+\dots+P(A\mid E_n)

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