(no subject)

[jgrafton]

Dear Lord...

I was arguing with a friend in another journal about my probability of using 4 unique user icons in 4 comments I made, and here's the reply I made:

Given that I have 15 different icons, there are 15 * 14 * 13 * (4 choose 2) permutations of only 2 of them the same, 15 * 14 * (4 choose 1) combinations [I meant permutations] for [only] 3 of them the same, and 15 combinations for 4 the same. This sums to 15 * 14 * 13 * 3 * 2 + 15 * 14 * 4 + 15 = 17235 possible choices.

The total number of permutations of 15 icons is 15^4, or 50625.

The probability that I choose at least 2 icons the same is thus 17235/50625 = 383/1125 or about .34. Thus probability states that it is more likely that I chose 4 unique icons, and not at least 2 of them the same.

I win.

Too much 251... I think I need to sleep.

(Also, I probably messed up my math somewhere, but don't tell mogrothir that.)

Comments

[ikeepaleopard]

Isn't that going to be 15*14*13 * 3 ways to have exactly 1 duplicated over 4 choices, since you pick the first three different then choose 1 of the three? Similarly the second would be 15 * 14 * 2.

[mogrothir.livejournal.com]

JEFF GOT OWNED

[jgrafton]

I'm not sure what he's arguing is correct, and even if it were, it would make the probability that I chose at least 2 icons the same even less than what I calculated.

Thus I win even more.

[jgrafton]

I'm not following what you're saying, exactly.

Say I use icons A, A, B, and C. There are 15 choices for A, 14 for B, and 13 for C. To count for ordering, I choose where to place B and C, hence 4 choose 2.

Next I use icons A, A, A, and B. I have 15 choices for A and 14 for B. I can place B in 4 choose 1 places.

Lastly, I just use A, A, A, A. Ordering doesn't matter here.


Do I have some faulty reasoning here?

[ikeepaleopard]

Oh, I forgot to account for ordering. Yeah, that makes sense.

[mogrothir.livejournal.com]

However, you forgot to mention that you're lazy as hell (as seen in your comments to prior journals / that post itself) and rarely change your icon for anything other than making posts in your own journal. So, even if the probability is mathematically high, it's realistically very low that you changed it four times.

OWNED BY THE REAL WORLD.

[jgrafton]

You have no proof of my icon habits in your post however, which may have been different.

[jgrafton]

I'll even argue that I did try to change my icon more often than normal for your post.

You have no proof to suggest otherwise.