ShmoopTube

00:03

It's a bird! It's a plane! It's Shmooperman...guy.

00:08

A fly is flying around this square board.

00:10

The length of the board is 36 centimeters.

00:13

If each of the lines is 1 centimeter thick, what is the probability that the fly will land on a line?

00:20

Round your answer to the nearest percent.

00:22

Here are the potential answers...

00:27

It’s not like flies lead the most exciting lives. Maybe this is just its way of telling

00:30

us that it’s… “board?” All right, so we’re told that each line

00:35

on this board is 1 centimeter thick.

00:36

Okay, so we’ve got this board that’s 36 centimeters long and 36 centimeters wide.

00:42

We’re looking for the ratio of space taken up by lines to the space taken up by…emptiness…

00:47

…so the first thing we should do is probably count up these lines, eh?

00:51

We’ve got seven from top to bottom…

00:53

…and another seven from left to right.

00:55

That’s 14 lines total.

00:57

If each line is 36 centimeters long…which this problem tells us it is…

01:02

…then we take 36 times 14, for a total of 504 centimeters.

01:06

But hold your horses.

01:08

What about all those places where the lines overlap?

01:11

Yeah, we’ll have to subtract those points from our total.

01:14

We have 7 lines criss-crossing another 7 lines, which gives us 49 total points of intersection.

01:18

504 minus 49 equals 455…which is how much space the one centimeter thick lines taken up.

01:26

To get the total area of the board, we just take 36 times 36… which comes out to 1,296.

01:33

Now we need our percentage…so we take 455 divided by 1,296…

01:39

…and wind up with 35 percent. Answer B.

01:42

Unfortunately for our hero, this board also happens to be a popular hang-out spot for Franny the Frog…

Full Transcript