# Probability problem

Acolyte
Posers and Puzzles 25 Jan '03 16:46
1. Acolyte
Now With Added BA
25 Jan '03 16:46
This one's not hard if you spot the answer, but I think it deserves a little explanation (sorry royalchicken, no elaborate proofs required):

Vaknso and Rhymester are playing a game. Vaknso tosses a coin 10 times, Rhymester only 9; both record the number of heads they got. If Vaknso gets more heads than Rhymester, he wins; otherwise Rhymester wins. Assuming neither cheats, what is the probability that Rhymester wins?
2. 25 Jan '03 19:00
50/50..π if im right π³if im wrong!
3. Acolyte
Now With Added BA
25 Jan '03 19:14
Originally posted by peterh
50/50..π if im right π³if im wrong!
But why 50/50?
4. Chris
Site Admin
25 Jan '03 19:172 edits
Originally posted by Acolyte
This one's not hard if you spot the answer, but I think it deserves a little explanation (sorry royalchicken, no elaborate proofs required):

Vaknso and Rhymester are playing a game. Vaknso tosses a coin 10 times, Rhymester only 9; both ...[text shortened]... uming neither cheats, what is the probability that Rhymester wins?
I'm afraid I don't know why. But the answer is 50/50, because there are 110 possible outcomes, and vaknso wins 55 of them. Actually there it is... some of them must be draws...

I cheated and resorted to programming to solve... (sorry about the formatting, this poorly designed site doesn't deal with indentation properly π )

int totalCombos = 0;
int vaknsoWins = 0;
for (int vaknso=0; vaknso&lt;=10; vaknso++)
{
for (int rhymester=0; rhymester&lt;=9; rhymester++)
{
totalCombos ++;
if (vaknso &gt; rhymester)
{
vaknsoWins ++;
}
}
}
float ratio = (float)vaknsoWins / totalCombos;

System.out.println(vaknsoWins + &quot;/&quot; + totalCombos + &quot; = &quot; + ratio);

5. Chris
Site Admin
25 Jan '03 19:19
So I completed the program to give me all the facts...

Vaknso Wins: 55/110 = 0.5
Draws: 10/110 = 0.09090909
Rhymester Wins: 45/110 = 0.4090909
6. Rhymester
and RedHotTed
25 Jan '03 19:251 edit
Well I'm no mathematician but if we tossed it the same number of times it would be 50%. I'm tossing it one less time so Vaknso would have the advantage - so less than 50% chance of me winning.
He's tossing it 10% more than me so he has 10% more chance of winning. So 6 to 4 on for Vaksno to win. 60% for Vaknso which leaves a 40% chance of me (Rhymester) winning.

Rhymester
7. 25 Jan '03 19:55
i reckon its 50/50- if they both had 9 each then 50/50 and they both have 50/50 on the extra go (the 19th go) theres no need for any more throws because someone would have won! surely there cannot be a draw on a toss of a coin?and surely there cant be a draw if best out of 19? im no mathematician either..so there could be plenty of thisπ³π³and this:'(:'(.....π
8. Chris
Site Admin
25 Jan '03 19:56
Originally posted by Rhymester
Well I'm no mathematician but if we tossed it the same number of times it would be 50%. I'm tossing it one less time so Vaknso would have the advantage - so less than 50% chance of me winning.
He's tossing it 10% more than me so he has 10% more chance of winning. So 6 to 4 on for Vaksno to win. 60% for Vaknso which leaves a 40% chance of me (Rhymester) winning.

Rhymester
And what about your draws... π
9. Chris
Site Admin
25 Jan '03 19:58
Originally posted by peterh
...surely there cant be a draw if best out of 19? im no mathematician either..so there could be plenty of thisπ³π³and this:'(:'(.....π
It's a draw if Vaknso gets 5 out of 10 and Rhymester gets 5 out of 9...
10. 25 Jan '03 20:07
p.s....if this is anything like the ''don''question ππ then im going to look a bit silly!π
11. Rhymester
and RedHotTed
25 Jan '03 20:181 edit
OK then 33.3% and that's my final offer π

I think the first 9 tosses would cancel each other out probability wise and I would have a 1 in 3 chance on the tenth toss.

Rhymester
12. royalchicken
CHAOS GHOST!!!
25 Jan '03 21:21
Acolyte-Don't you think it a bit dangerous to be pitting vaknso and Rhymester against each other π? There could be riots...
13. Rhymester
and RedHotTed
25 Jan '03 23:49
Originally posted by royalchicken
Acolyte-Don't you think it a bit dangerous to be pitting vaknso and Rhymester against each other π? There could be riots...
Baggies I keep the coins when it's all over! π

Rhymester
14. Rhymester
and RedHotTed
29 Jan '03 08:46
Originally posted by Rhymester
OK then 33.3% and that's my final offer π

I think the first 9 tosses would cancel each other out probability wise and I would have a 1 in 3 chance on the tenth toss.

Rhymester
So, was I right?
15. Acolyte
Now With Added BA
29 Jan '03 09:16
The answer is 50/50: note that if they both get the same number of heads, Rhymester wins.
Vaknso gets an extra toss; if he gets tails, he's at a disadvantage because he now has to get more heads than Rhymester to win; if he gets heads, he's at an advantage because (over the remaining 9 tosses each) Rhymester has to get more heads than him to win.