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dimri10
In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.06 at any given 10
minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are
the odds that the panel would be turned off within the first 10 minutes after it was switched
on?
(A) 1-0.06^10
(B) 1-0.94^10
(C) (1-0.94)^10
(D) 0.06
(E) 1-10*0.06

ans B.

Prob that light will not turned off = 0,94^10. Hence prob (turn off) = 1 - prob (not turn off).
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dimri10
In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.06 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?

(A) 1-0.06^10
(B) 1-0.94^10
(C) (1-0.94)^10
(D) 0.06
(E) 1-10*0.06

P (Panel woud be turned off within first 10 mins) = 1 - P (Panel would not be turned off within first 10 mins)

Only if all 10 light bulbs work will the panel not be turned off within the first 10 mins.
Probability of a light bulb working = 1 - 0.06 = 0.94
Probability of 10 light bulbs working for the first 10 mins \(= (0.94)^{10}\)

P (Panel woud be turned off within first 10 mins) \(= 1 - (0.94)^{10}\)

Answer (B)
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Karishma,

What is that you are counting in excess if you add each individual prob of failing.
.06 (10) = .60

I got to the right answer by estimation. Figured out that .96^10 will be near to .50. And 1-.50 was near my .60 above.

Your explanation is clear. Prob of at least 1 failing= 1- Prob of all behaving ok.

Was just curious on what accounts for the diff between .46 (the correct answer) and .60

Regards,

Juan C. Avellan
KarishmaB


P (Panel woud be turned off within first 10 mins) = 1 - P (Panel would not be turned off within first 10 mins)

Only if all 10 light bulbs work will the panel not be turned off within the first 10 mins.
Probability of a light bulb working = 1 - 0.06 = 0.94
Probability of 10 light bulbs working for the first 10 mins \(= (0.94)^{10}\)

P (Panel woud be turned off within first 10 mins) \(= 1 - (0.94)^{10}\)

Answer (B)
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