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Manhattan 700 + Need experts' help ONLY

by btgyes » Sun Jan 30, 2011 2:10 am
EXPERTS,

Before looking at ques, please consider these two scenario

1.
------------------------------------------
one person throws a coin.
probability of coming Head = 1/2
Probability of coming Tail = 1/2
------------------------------------------

2.
-------------------------------------------------
Two teams playing.
probability that team A will win = 1/2
Probability that team B will win = 1/2
-------------------------------------------------

Now i want to EMPHASIZE one point here that
this is very much possible that COIN may stand VERTICALLY(that mean no OUTPUT)
OR
there may be a TIE between Team A and Team B

but WE NEVER EVER TOOK THIS POSSIBILITY EQUAL TO 1 / 3

in simple words, we never considered that COIN will stand vertically literally even it is very much possible
and we never consider tie option . We always assume this possibility ZERO even if it is not EXACTLY.



I HOPE EXPERTS UNDERSTOOD MY POINT.


Plz elaborate what's wrong here.....

THANKS...!
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by Anurag@Gurome » Sun Jan 30, 2011 4:49 am
First of all, I do not agree on your points.

For tossing of coin, yes, we do not consider the event that the coin will stand on its edge vertically as it is a very rare event. Whereas getting a head or tail is much more common. Hence we take the probability of such event as zero. What do I mean by "rare"? For example say if you toss a coin 10,000 times, you'll get either a head or tail in almost all the tosses. But you'll find the coin is standing vertically on its edge only twice or thrice. Hence, probability of such an event = 3/10,000, which is almost equal to zero. If you consider a less number of tosses, say 10, you may find that the coin never stands vertically on its edge. Thus practically the probability is zero. Thus ideally this event should have a probability of occurrence = 1/3, b as practically it never happens, we take the probability as zero.

But for match between two teams or players three outcomes (win, loss, tie) are equally probable. We never discard the probability of tying unless otherwise mentioned. For example, if two persons simultaneously toss two coins 10, 000 times and the one with head wins, then we'll see the number of wins, ties or losses for one of them are almost same. Hence, the three events have equal probability.

Thus for this question you have to consider the event that both of the players say the same word, i.e. they tie.
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by btgyes » Sun Jan 30, 2011 5:38 am
Anurag@Gurome wrote:First of all, I do not agree on your points.

For tossing of coin, yes, we do not consider the event that the coin will stand on its edge vertically as it is a very rare event. Whereas getting a head or tail is much more common. Hence we take the probability of such event as zero. What do I mean by "rare"? For example say if you toss a coin 10,000 times, you'll get either a head or tail in almost all the tosses. But you'll find the coin is standing vertically on its edge only twice or thrice. Hence, probability of such an event = 3/10,000, which is almost equal to zero. If you consider a less number of tosses, say 10, you may find that the coin never stands vertically on its edge. Thus practically the probability is zero. Thus ideally this event should have a probability of occurrence = 1/3, b as practically it never happens, we take the probability as zero.

But for match between two teams or players three outcomes (win, loss, tie) are equally probable. We never discard the probability of tying unless otherwise mentioned. For example, if two persons simultaneously toss two coins 10, 000 times and the one with head wins, then we'll see the number of wins, ties or losses for one of them are almost same. Hence, the three events have equal probability.

Thus for this question you have to consider the event that both of the players say the same word, i.e. they tie.

Thanks for comment ...

i do agree with the specific example you provided.

but do you really think that

if there are 100 matches played between two team ( cricket , football , tennis etc.)

then 33 % chances are for TIE.

Practically , there will be 3-4 tie matches at the very best.

so Probability will be 3/100 that is obviously negligent.

Thats why i didn't considered this probability.

Please comment.

Thanks a lot...
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by Anurag@Gurome » Sun Jan 30, 2011 5:50 am
btgyes wrote:but do you really think that

if there are 100 matches played between two team ( cricket , football , tennis etc.)

then 33 % chances are for TIE.
Yes, not exactly 33%, but the number of ties, wins and losses will be comparable. For example, say 28, 40 and 32 respectively.

Here is a small exercise for you.
  • 1. Toss a coin 50 times and write the results in a paper in pairs according to their occurrence, like (H, T), (H, H), (T, H) ... etc.
    2. Count the number of pairs in which the first one is H, i.e. a win
    3. Count the number of pairs in which the first one is T, i.e. a loss
    2. Count the number of pairs in which the both are same, i.e. a tie
See for yourself.

You can do it with two different coins with a friend or you can play the rock-paper-scissor with someone for 20 or 25 times. You'll find that a tie is equally probable as win or loss.

Also see how many times the coin stands vertically on its edge. :)
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by btgyes » Sun Jan 30, 2011 6:04 am
Anurag@Gurome wrote:
btgyes wrote:but do you really think that

if there are 100 matches played between two team ( cricket , football , tennis etc.)

then 33 % chances are for TIE.
Yes, not exactly 33%, but the number of ties, wins and losses will be comparable. For example, say 28, 40 and 32 respectively.

Here is a small exercise for you.
  • 1. Toss a coin 50 times and write the results in a paper in pairs according to their occurrence, like (H, T), (H, H), (T, H) ... etc.
    2. Count the number of pairs in which the first one is H, i.e. a win
    3. Count the number of pairs in which the first one is T, i.e. a loss
    2. Count the number of pairs in which the both are same, i.e. a tie
See for yourself.

You can do it with two different coins with a friend or you can play the rock-paper-scissor with someone for 20 or 25 times. You'll find that a tie is equally probable as win or loss.

Also see how many times the coin stands vertically on its edge. :)
I understand that coin standing will be rare...

BUT

TIE chances between two team playing any sports ( EXCEPT COIN THROWING) will be FAR LESS than 33 %

this is my main point.

Plz comment on this.

Thanks
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by Anurag@Gurome » Sun Jan 30, 2011 10:16 am
btgyes wrote:
Anurag@Gurome wrote:
btgyes wrote:but do you really think that

if there are 100 matches played between two team ( cricket , football , tennis etc.)

then 33 % chances are for TIE.
That depends on the nature of the game and also on strength of players or teams.

If the game is cricket, then the chance for a tie is very small.
If the game is football, then the chance for a tie is small but not very small.
Same goes for other games.

Let's take an example.
If two strong teams with comparable strength plays football, then you can expect that most of the time the game will end in a tie. Because the score in a football game is generally within a range of 0-5. Hence it's not rare that their score will be same. But for cricket, the total run of a team generally within a range 250-350. Hence it's rare that two teams will score same.

As far as the game is rock-paper-scissor between two player and both player have equal probability of choosing a particular word, a tie is as common as a win or a loss.
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by btgyes » Thu Feb 03, 2011 5:15 am
Anurag@Gurome wrote:
btgyes wrote:
Anurag@Gurome wrote:
btgyes wrote:but do you really think that

if there are 100 matches played between two team ( cricket , football , tennis etc.)

then 33 % chances are for TIE.
That depends on the nature of the game and also on strength of players or teams.

If the game is cricket, then the chance for a tie is very small.
If the game is football, then the chance for a tie is small but not very small.
Same goes for other games.

Let's take an example.
If two strong teams with comparable strength plays football, then you can expect that most of the time the game will end in a tie. Because the score in a football game is generally within a range of 0-5. Hence it's not rare that their score will be same. But for cricket, the total run of a team generally within a range 250-350. Hence it's rare that two teams will score same.

As far as the game is rock-paper-scissor between two player and both player have equal probability of choosing a particular word, a tie is as common as a win or a loss.
THanks a lot...!
I got yr point... great...

still one last point...

i haven't heard this game called rock-paper-scissor . I got the concept but sometimes when we dont have much idea what game is all about then

do we need to take TIE option take into accounted... ie. 33 %


BY the way, wharever the chances of winning or losses of a certain team in a certain game,

we just need to take TIE option in default (unless it is coin throwing).. RIGHT SIR... This is what i got....

Thanks
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