2 [20 points, 5 each) A randomly selected light bulb of a certain brand has prob

Question

2 [20 points, 5 each) A randomly selected light bulb of a certain brand has probabilities 0.9,087 n 0.78 of lasting at least 1000, at least 2000, and at least 3000 hours, respectively (a) What is the probability that a new light bulb will last between 1000 and 2000 hours b) What is the probability that a light bulb that is known to have lasted 1000 hours so far lasts at least another 1000 hours? (c) Supppose that l check in en a light bulb at X00 hours after it was tururd on, and I find that it has burnt out. What is the probability that it lasted at least 1000 hours? (d) Which is more likely to survive the next 1000 hours: a new lightbulb or a 1000-hour-old lightbulb

Explanation / Answer

P( last >= 1000) = 0.9
P( last >= 2000) = 0.87
P( last >= 3000) = 0.78

a) Probability that a new lightbulb last between 1000 and 2000 hours is computed here as:

P( last >= 1000) - P( last >= 2000)

= 0.9 - 0.87 = 0.03

Therefore 0.03 is the required probability here.

b) P( last >= 2000 | last >= 1000) = P( last >= 2000 ) / P( last >= 1000 ) = 0.87 / 0.9 = 0.9667

Therefore 0.9667 is the required probability here.

c) P( last >= 1000 | last <= 3000 ) = P(last >= 1000 and last <= 3000 ) / P( last <= 3000)
= (0.9 - 0.78 ) / (1 - 0.78 ) = 0.4212

Therefore 0.4212 is the required probability here.

d) For a new lightbulb, P( last >= 1000 ) = 0.9

For a 1000 hour old bulb, P( last >= 1000) =

P( last >= 2000 | last >= 1000) = P( last >= 2000 ) / P( last >= 1000 ) = 0.87 / 0.9 = 0.9667

Therefore the bulb already which survived 1000 hours is more likely to survive another 1000 hours than a new bulb.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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