Suppose that Upper A 1A1 and Upper A 2A2 form a partition of the sample space S

Question

Suppose that Upper A 1A1 and Upper A 2A2 form a partition of the sample space S with Upper P left parenthesis Upper A 1 right parenthesis equals 0.75PA1=0.75 and Upper P left parenthesis Upper A 2 right parenthesis equals 0.25PA2=0.25. If E is an event that is a subset of S and Upper P left parenthesis Upper E vertical line Upper A 1 right parenthesis equals 0.06PE A1=0.06 and Upper P left parenthesis Upper E vertical line Upper A 2 right parenthesis equals 0.09PE A2=0.09?, find Upper P left parenthesis Upper E right parenthesisP(E). Upper P left parenthesis Upper E right parenthesisP(E)equals=nothing

Explanation / Answer

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P(A1) = .75

P(A2) = .25

P(e|A1)= .06

P(e)=?

P(e) = p(e|A1) *p(A1) + p(e|A2)*p(A2)

P(e|A2) = .09

So, p(e) = .06*.75 + .09*.25 = .045+.225= .270

So answer is .270

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