light bulb fails

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Mar 12, 2012 2:28 am

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 id 0.06, what is the probability that the string of light bulbs 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

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Source: Beat The GMAT — Problem Solving | Mon Mar 12, 2012 2:28 am

killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Mon Mar 12, 2012 2:38 am

required probability= 1- probability that all 10 bulbs dont fail
= 1- (1-0.06)^10
= 1- 0.94^10

IMO E

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Mar 12, 2012 5:12 am

sanju09 wrote: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 id 0.06, what is the probability that the string of light bulbs 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

Probability of 1 light bulb failing during time period T = 0.06
So, probability of 1 light bulb NOT failing during time period T = 1 - 0.06 = 0.94

For the string to be successful, all the light bulbs should pass because if any individual light bulb fails, the entire string fails.
Probability of 10 light bulbs NOT failing = (0.94)^10
Probability of 10 light bulbs failing = 1 - Probability of 10 light bulbs NOT failing = 1 - (0.94)^10

The correct answer is E.

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kul512: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Sep 29, 2011 5:15 amFollowed by: 1 member; Thanked: 7 times; GMAT Score:740

by kul512 » Mon Mar 12, 2012 1:34 pm

Just adding some information-

One thing which must be taken care is that failing of one bulb is not going to affect the failing of other bulb. means these events are mutually exclusive events and that's why we need to use
"1- none fails" formula rather than "1st fails OR 2nd fails OR 3rd fails....".

Means we cants simply add all the probability.

Sometimes there is very fine line between right and wrong: perspective.

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