A string of 5 different colored light bulbs is wired in such

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e-GMAT

A string of 5 different colored light bulbs is wired in such a way that if any two-consecutive light bulb fails, then entire string fails. If for each individual light bulb, the probability of not failing during time period T is 0.85, what is the probability that the string of light bulbs will fail during the time period T?

A. 0.0225
B. 0.09
C. 0.225
D. 0.25
E. 0.5

OA B.

[deloitte247]

Given that ;
There is a string of 5 different colored light bulbs.
The string fails if any two consecutive light bulb fails .
The probability of each bulb not failing during a period of time T = 0.85
Question=
Find the probability that the string of light will fail during the period time T.

Answer =
Probability of a bulb not failing = 0.85
Probability of a bulb failing = 0.15
Total ways in which 2 consecutive light bulbs can fail in a string of 5 bulbs = 4
Probability that the string of light bulbs will fail,
= Probability of one bulb fail * Probability o another consecutive bulb fail * ways in which 2 consecutive bulb can fail.
= 0.15 * 0.15 * 4
=0.09
Option B is CORRECT.

[Jay@ManhattanReview]

e-GMAT

A string of 5 different colored light bulbs is wired in such a way that if any two-consecutive light bulb fails, then entire string fails. If for each individual light bulb, the probability of not failing during time period T is 0.85, what is the probability that the string of light bulbs will fail during the time period T?

A. 0.0225
B. 0.09
C. 0.225
D. 0.25
E. 0.5

OA B.

The string would fail if 1st and 2nd; 2nd and 3rd; 3rd and 4th; or 4th and 5th bulbs together fail.

Given that the probability of not failing during the time period T is 0.85, we have the probability of failing during the time period T = 1 - 0.85 = 0.15.

1. Probabality of failing of 1st and 2nd bulbs = 0.15 * 0.15 = (0.15)^2;
2. Probabality of failing of 2nd and 3rd bulbs = (0.15)^2;
3. Probabality of failing of 3rd and 4th bulbs = (0.15)^2;
4. Probabality of failing of 4th and 5th bulbs = (0.15)^2

Thus, the probability that the string of light bulbs will fail during the time period T = 4*(0.15)^2 = 4*0.025 = 0.09

The correct answer: B

Hope this helps!

-Jay
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