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555-605 (Medium)|   Probability|         
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GMATCoachBen
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A string of 10 lightbulbs is wired in such a way that if any individua 28 Nov 2021, 23:28
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tkorzhan1995
GMATCoachBen, can you please help to clarify what is wrong with my approach?


I originally selected B (0.06^10) for this question. Can you please explain how the question may be worded differently, so B is a correct answer?
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tkorzhan1995, your answer would be correct if the problem said "the string fails ONLY if ALL of the individual lightbulbs fail". Then, we would need ALL ten to fail, so we would be multiplying the probabilities for each failure: (0.06^10).

However, the wording of the question says "if ANY individual lightbulb fails, the entire string fails."

BrentGMATPrepNow wrote a great solution here: https://gmatclub.com/forum/a-string-of- ... l#p1845682

In particular, his advice below is helpful in general:
BrentGMATPrepNow
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
P(at least 1 lightbulb fails) = 1 - P(zero lightbulbs fail)
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A string of 10 lightbulbs is wired in such a way that if any individua 21 Jul 2023, 00:14
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P(1 light bulb fail)=0.06
Also P(1 light bulb fail)+P(1 light bulb no fail)=1
P(1 light bulb no fail)=1- P(1 light bulb fail)=1-0.06=0.94
P(string not fail)=P(1 light bulb no fail)=(1-0.06)^10 (since no. of bulbs = 10)
i.e. P(no bulb fail)=(0.94)^10

Therefore since P(string not fail)+P(string fail)=1
P(string fail)=1-P(string not fail)
P(string fail)=1-(0.94)^10

Hence E
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ManifestDreamMBA
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A string of 10 lightbulbs is wired in such a way that if any individua 09 Feb 2025, 11:17
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if any individual lightbulb fails, the entire string fails is equivalent to if at least 1 lightbulb fails, the entire string fails. For the string of lightbulbs to work, all bulbs should not fail
P(Bulb fails) = 0.06
P(Bulb doesn't fail)= 1- 0.06= 0.94
P(All 10 bulbs don't fail = lightstring works) = 0.94^10
P(String of lightbulbs fail) = 1 - 0.94^10

massi2884
A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T is 0.06, what is the probability that the string of lightbulbs will fail during time period T ?

A. \(0.06\)

B. \((0.06)^{10}\)

C. \(1 - (0.06)^{10}\)

D. \((0.94)^{10}\)

E. \(1 - (0.94)^{10}\)

PS03508

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I know it's not among the answer choices, but could you please tell me what's wrong with thinking that the result should be
0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 10*0.06 = 0.6 ?
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Ziniya
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A string of 10 lightbulbs is wired in such a way that if any individua 17 May 2025, 06:58
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Bunuel, can we solve it using binomial probability?
Bunuel
massi2884
A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?

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

I know it's not among the answer choices, but could you please tell me what's wrong with thinking that the result should be
0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 + 0.06 = 10*0.06 = 0.6 ?

The string of light bulbs will fail if at least one light bulb fails. Thus, let's determine the probability of the opposite scenario and subtract this value from 1.

The opposite scenario is when none of the 10 light bulbs fail. Given that the probability of each light bulb not failing is 1 - 0.06 = 0.94, the probability that none of the 10 light bulbs fail is 0.94^10.

Therefore, the probability that at least one light bulb fails is 1 - 0.94^10.

Answer: E.

You should've realized that your reasoning was incorrect due to a simple factor. Consider the case where we have 100 light bulbs instead of 10, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6. However, this is impossible as the probability of an event can never exceed 1 (100%).

Hope it's clear.
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A string of 10 lightbulbs is wired in such a way that if any individua 16 Dec 2025, 03:29
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Why the other options are wrong (quick intuition)

A. 0.06
→ That’s the failure probability of one bulb, not the whole string.

B. (0.06)10
→ That’s the probability all 10 bulbs fail, which is much rarer than “at least one fails”.

C. 1 − (0.06)10
→ That’s “not all 10 fail” — includes many cases where some work and some fail. Not the event we want.

D. (0.94)10
→ That’s the probability the string does not fail.
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