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

Question

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. \(1-(0.96)^{10}\)

Show Answer

Official Answer

E

A. 0.04
B.  (0.04)^{10} 
C.  1-(0.04)^{10} 
D. 0.96
E.  1-(0.96)^{10}

IanStewart · Accepted Answer

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.

PSKhore · Answer

But if it's mentioned that  i   f one matchstick falls, the whole string will fall,  why will there be any other cases?

IanStewart · Answer

The question is not worded correctly, but I assume it's trying to say that for each of the ten matchsticks, there is a 0.04 probability the matchstick falls. So there are really eleven different cases -- zero matchsticks fall, one matchstick falls, two matchsticks fall, and so on, up to all ten falling. If you wanted to solve this problem directly, you would need to add ten different probabilities -- the probability that one falls, the probability that two fall, the probability that three fall, and so on, since in every one of those ten cases, the string of matches will fall. Most of those probabilities are difficult to calculate (you would need to use binomial probability concepts), which is why I solved the question by finding the probability that no matches fall, then subtracted that from 1.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards