Probability Problem for Fun

[Debater Slayer]

Suppose you have a round table with a radius of 20 inches. There's a bottle on the table, but you don't know exactly on which spot. However, you know that the bottle has an equal probability of being on any spot on the table.

You can only reach 10 inches in with your hand such that you stop right on the edge of the smaller circle, like this:

Spoiler: Large image

If you wear a blindfold and encircle the table while reaching for the bottle, what is the probability that it will be within your reach?

 

[lewisnotmiller]

Spoiler

25%

[Edit : sorry, flip that. 75%]

 

[Debater Slayer]

Spoiler

25%

[Edit : sorry, flip that. 75%]

Use spoilers!

I won't deny or affirm any answer yet.

 

[Augustus]

If you wear a blindfold and circle the table while reaching for the item, what is the probability that it will be within your reach?

Spoiler

75%, the outer circle area is 75% of the table area

 

[Debater Slayer]

Spoiler

75%, the outer circle area is 3 times bigger than the middle?

Spoiler

Won't say just yet, but let's just say I like that method.

 

[Viker]

Spoiler

I concur with 75%. But, I am currently dizzy, laying in bed, feet elevated and dimwitted

 

[John53]

Fun?

 

[Daemon Sophic]

Spoiler: Answer

It’s about area. The area of the smaller (10 inch radius circle) is 100pi. The overall circle (20 inches in radius) is 400pi.
But I can’t reach the 100pi area smaller circle, thus the remaining area I can reach is 300pi. The ratio of areas is thus 3:1. (i.e, I can get to 75% of the total table area).

 

[icehorse]

i have my answer, but i don't know how to post a spoiler

 

[Subduction Zone]

i have my answer, but i don't know how to post a spoiler

You write the word "spoiler" within a set of square brackets. These doodlybobs: [ ]

You do not need to even use a closing spoiler but if you want to write something afterwards type [/ and then "spoiler" and then your other bracket ].

No spaces or other punctuation in it.

 

[icehorse]

Spoiler

75%

 

[Vinayaka]

Spoiler

75%?

 

[ChristineM]

i have my answer, but i don't know how to post a spoiler

It's also in the pull down [+] menu between insert movie and insert media icons

 

[exchemist]

Spoiler

75%, the outer circle area is 75% of the table area

Agree.

 

[Brickjectivity]

Spoiler

(20^2 - 10^2)/20^2
answer: 0.75 chance

 

[Jedster]

Spoiler: Spoiler

Removing the limitation, the probability is 1. Introducing the limitation reduces the touchable area by 1/4, hence the probability is 1 - 1/4 = 3/4. QED(?)

 

[Debater Slayer]

The correct answer is indeed 75%! The area of the annulus, which is the region between the two concentric circles, represents 75% of the total area of the table (i.e., the bigger circle) in this case.

 

[Debater Slayer]

Spoiler: Spoiler

Removing the limitation, the probability is 1. Introducing the limitation reduces the touchable area by 1/4, hence the probability is 1 - 1/4 = 3/4. QED(?)

This is a great way to frame the problem, yes.

 

[Vinayaka]

The correct answer is indeed 75%! The area of the annulus, which is the region between the two concentric circles, represents 75% of the total area of the table (i.e., the bigger circle) in this case.

When I drove a tractor or farm machine around and around a square or rectangular field, I tried to calculate (in my head) when I was half done. It killed the time. I remember aworking for a neighbour on a half section (half mile by one mile) field that had no sloughs, nor rocks, nothing. It was boring, and took about 2 8 hour days. The machinery in those days was smaller.

 

[icehorse]

When I drove a tractor or farm machine around and around a square or rectangular field, I tried to calculate (in my head) when I was half done. It killed the time. I remember aworking for a neighbour on a half section (half mile by one mile) field that had no sloughs, nor rocks, nothing. It was boring, and took about 2 8 hour days. The machinery in those days was smaller.

Ah... sections and townships and acres and rods and chains and fathoms and..