#beautyofpie

Question

There is two parallel lines and a matchstick. The constant distance between these two lines is equal to the the length of the matchstick.

If the matchstick is dropped between the two lines randomly many times then what would be the probability that the matchstick would

intersect the lines(any of it).The answer is .64 but I am not sure Please explain..

Answer 1

I think i found the solution and it is interesting...

Theorem of the Buffon's needle.

Suppose we have a floor made of parallel strips of wood, each the same width 2b, and we drop a needle of length 2a onto the floor. The probability that the needle will lie across a line between two strips is  (2a/3.14b).

for more see http://www.pi314.net/eng/buffon.php
So the answer would be (2/3.14)=.64
 

Comments

@Amit. But the question says that the distance between the parallel sticks should also be 2a. I didnt get Buffon's solution.

---

Read the que: The constant distance between these two lines is equal to the the length of the matchstick.

thats why a=b here,and our assumption is matchstick have negligible width.So I think Buffon's solution works b'coz  a=b Or 2a=2b at the end it has to cancel out.

Answer 2

there are 3 possible outcomes

outcome 1 = either match stick intersects line 1

outcome 2 = either match stick intersects line 2

outcome 3 = or it can in middle and do not intesect any line

favourable outcomes = 2 (i.e is outcome1, outcome2)

probability = 2/3 = .666666

Comments

It is interesting thats why i have shared and searched for this que since last 3 days .I think this is the solution.