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?
Originally posted by AcolyteI'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...
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);
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
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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 this😳😳and this:'(:'(.....😉
Originally posted by RhymesterAnd what about your draws... 😉
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
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.