5. + -/1 points DevoreStat9 2.E.078. My Notes Ask Your Teacher A boiler has five

Question

5. + -/1 points DevoreStat9 2.E.078. My Notes Ask Your Teacher A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.91. Assume independent operation of the valves. Calculate P(at least one valve opens). (Round your answer to eight decimal places.) Calculate P(at least one valve fails to open). (Round your answer to four decimal places.) Need Help?Read It Talk to a Tutor 6. 0/1 points | Previous Answers DevoreStat9 2.E.079. My Notes Ask Your Teacher Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump will fail is 0.30, and the probability that only the newer pump will fail is 0.15. What is the probability that the pumping system will fail on any given day (which happens if both pumps fail)? (Round your answers to four decimal places.) smaller answer 0.045 larger answer 0.045 Need Help? Read ItTalk to a Tutor

Explanation / Answer

5)

P(at least one valves opens) =1-P(none opens)=1-(1-0.91)5 =0.99999410

P(at least one valve fails to open)=1-P(all opens)=1-0.915 =0.3760

6)let probability onlder and newer works are a and b

hence P(only older fails)=P(older fails)*P(newer not)=(1-a)*b =0.30

P(only smaller fails)=P(newer fails)*P(older not)=(1-b)*a =0.15

solving above: a=0.25 ,0.6

b=0.4 ,0.75

therefore smaller number =(1-a)*(1-b) =(1-0.6)*(1-0.75)=0.1

larger answer =(1-0.25)*(1-0.4)= 0.45

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