I have two servers at a grocery store. P(server 1) is 0.4. P(server 2) is 0.6. P(time is less than 5 min | server 1) is 1. P(time is less than 5 min | server 2) is 4/9. What is P(server 1 | time is less than 5 min)?

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Answer 1 · 2018-03-13T17:19:38

$0.6$ .

Suppose that, the events

$"Server 1="A," Server 2="B," &, Time less than 5 minutes="C$ .

We are given that,

$P(A)=0.4, P(B)=0.6, P(C|A)=1, P(C|B)=4/9$ .

Then, $P(C)=P(A)P(C|A)+P(B)P(C|B)$ ,

$=4/10*1+6/10*4/9$ ,

$rArr P(C)=2/3$ .

$"Now, The Reqd. Prob.="P(A|C)=(P(AnnC))/(P(C))..."[Defn.]"$ ,

$={P(C|A)*P(A)}/(P(C))$ ,

$={(1)(0.4)}/(2/3)$ ,

$=0.6$ .