- 25 Jan '03 16:46This 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? - 25 Jan '03 19:17 / 2 edits

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

int totalCombos = 0;

int vaknsoWins = 0;

for (int vaknso=0; vaknso<=10; vaknso++)

{

for (int rhymester=0; rhymester<=9; rhymester++)

{

totalCombos ++;

if (vaknso > rhymester)

{

vaknsoWins ++;

}

}

}

float ratio = (float)vaknsoWins / totalCombos;

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

- 25 Jan '03 19:25 / 1 editWell 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 - 25 Jan '03 19:55i 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 thisand this:'(:'(.....
- 25 Jan '03 19:56

And what about your draws...*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 - 29 Jan '03 09:16The 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.