The numbers in the question are wrong. It says you pulled something
out of the box and put it back in the box 100 times. The total of
everything you pulled out should be 100, but it says you got
(32 + 62) = 94 things.
I'm going to change the numbers slightly, so you'll see how to do it.
We're going to say that you get blue ones 33 times, and you get
red ones 67 times. That's better, because (33 + 67) = 100 .
When you do the experiment, the things in the box are shaken and
completely mixed up, and when you reach in to pick one, you always
keep your eyes closed so you don't see what you're getting. The
choice is always "random". That means what you get is determined
completely by chance, not by anything you do.
Then the result of your experiment is:
-- A blue thing comes out 33 times in 100 draws.
That's 33% of the time.
-- A red thing comes out 67 times in 100 draws.
That's 67% of the time.
If the choice is really random chance every time, then the only thing
that can influence what you get is how many of each thing is in the box.
Whatever there are more of, you'd expect to get more often. Whatever
there's less of, you'd expect to get less often.
-- You pulled things out of the box 100 times.
-- You got blue things 33% of the times.
-- You got red things 67% of the times.
-- Now, you take an educated guess, and you tell everyone:
"I estimate that roughly 33% of the things in the box are blue,
and roughly 67% of the things in the box are red."
Then you ask: "How many things are in the box all together ?"
There are 20 things in the box all together, Makookoo.
"Well OK then. 33% of 20 things is 6-2/3 things. But all the things
in the box are whole things. There aren't any pieces of things. So I'll round my estimate to the nearest whole thing. 6-2/3 rounds to 7 . . . Roughly 7 of the things in the box are blue.
And furthermore . . .
"67% of 20 things is 13.4 things. But all the things in the box are
whole things. There aren't any pieces
of things. So I'll round my
estimate to the nearest whole thing. 13.4 rounds to 13 . . . Roughly
13 of the things in the box are red."
