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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?
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).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?
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)
That is, P(Event A happening) = 1 - P(Event A not happening)
P(at least 1 lightbulb fails) = 1 - P(zero lightbulbs fail)
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
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
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
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
A. \(0.06\)
B. \((0.06)^{10}\)
C. \(1 - (0.06)^{10}\)
D. \((0.94)^{10}\)
E. \(1 - (0.94)^{10}\)
PS03508
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 ?
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 ?
