Question
Asked Oct 1, 2019
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This problem involves a sample space S with two events, E and F.

Assume that Pr[E]=17/30, Pr[F|E]=10/17, and Pr[E′∩F′]=7/30 

(1) Pr[F]=

 


(2) Pr[E∩F]=

 

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Expert Answer

Step 1

Result used:

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1. Р(4|в)- Р(4оB) or P(4nB)- P(в).P(4|в) Р(В) 2. P(nB)-P(AUB) and P(4 B)-1- P((4UB)) 3. Р(4ОВ)- Р(4)+ P(В)- Р(4n В)

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Step 2

Use result 1 to find the probability of E∩F as follows.

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Pr(E F) Pr(E) Pr(F\E) 17 10 30 17 1 3

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Step 3

Use result 2 to find the probabil...

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Pr(EnF)= Pr(EUF)) 7 30 Pr(EF)1-Pr (EUF) 7 =1- 23 30 |30

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