29. Smoke Detectors: Suppose a certain brand of smoke detector functions properl

Question

29. Smoke Detectors: Suppose a certain brand of smoke detector functions properly 85% of the time. Now to be extra safe, I have installed 3 of these smoke detectors in my bedroom. ' E Calculate the following probabilities rounding your answer to 3 significant digits (a) What is the probability that all three smoke detectors function properly on the night of a fire? the three smoke detectors functions properly on the night of a fire? (c) Comment on the difference in the probabilities found in parts (a) and (b). Which probability is more relevant to the situation?

Explanation / Answer

a)

P(all three function properly on night of fire)=0.85*0.85*0.85=0.614125

b)

P(at least one work properly)=1-P(none works)=1-(1-0.85)3 =0.996625

c)

here probability in part b is more relevent; as from safety prespective we are more interested in getting a alarm against firm and not how many signal we receives,

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.