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Nancy places ten matchsticks next to each other which are rested again

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Joined: 13 Oct 2019
Posts: 21
Location: India
GPA: 4
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Nancy places ten matchsticks next to each other which are rested again  [#permalink]

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New post 17 Jan 2020, 00:26
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

29% (01:02) correct 71% (01:21) wrong based on 24 sessions

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Nancy places ten matchsticks next to each other which are rested against a wall. If one matchstick falls, the whole string will fall. If the probability that the matchstick will fall in 5 seconds is 4%, what is the probability that the string of matchsticks will fall in 5 seconds?

A. 0.04
B. \((0.04)^{10}\)
C. \(1-(0.04)^{10}\)
D. 0.96
E. \(1-(0.96)^{10}\)
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Joined: 24 Jun 2008
Posts: 2011
Re: Nancy places ten matchsticks next to each other which are rested again  [#permalink]

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New post 17 Jan 2020, 05:11
If the probability a match will fall is 0.04, the probability it will not fall is 0.96. So the probability all ten matches will remain standing is (0.96)^10, and subtracting from 1, we find that 1 - (0.96)^10 is the probability one or more matches will fall (and thus the string will fall).

It's only really practical to do the problem "backwards", by working out the probability first that we do not get the result the question asks for, then subtracting from 1, because doing the problem directly involves a lot of cases.
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Re: Nancy places ten matchsticks next to each other which are rested again   [#permalink] 17 Jan 2020, 05:11
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Nancy places ten matchsticks next to each other which are rested again

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