# Probability

• September 5th, 2014, 09:18 AM
Ashwin
Probability
Hi,
If three coins are tossed simultaneously, the following are possible:
{HHH, HHT, HTH, TTH, TTT, THH, THT, HTT}
In this case n(S) = 8.
It can be written in smaller cases.
If I say, 10 coins are tossed simultaneously, how do I calculate the number of possibilities? Is there a formula to do the same?

Thanks
Ashwin
• September 5th, 2014, 01:14 PM
MagiMaster
Each new coin doubles the number of possibilities, so it's just 2^n.
• September 7th, 2014, 12:39 AM
Ashwin
Well, that seems to work in the case of coins. What if two dice are thrown, then there are 36 possibilities.
So is there a general formula for all of these cases?
• September 7th, 2014, 02:04 AM
Dywyddyr
Two dice = 62 possible results.
Three dice = 63.
Same rule.
Number of possible results of one [coin/ die]number tossed/ rolled.
• September 7th, 2014, 01:50 PM
Guitarist
Ya well, there is a slight problem here (in mathematical terms)

Suppose it is true that tossing coins, each with 2 possible outcomes gives a total of possible outcomes.

Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

Does it help to note that tossing coins just once has exactly the same number of possible outcomes as tossing a single coin times? Well, tossing a single coin zero times reveals the starting face, that is only outcomes.

• September 7th, 2014, 01:55 PM
Dywyddyr
Quote:

Originally Posted by Guitarist
Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

I just spent fifteen minutes tossing zero coins.
And always got the same result.
That's close enough for me.
• September 7th, 2014, 01:57 PM
PhDemon
^^ Spot the engineer :p
• September 7th, 2014, 02:02 PM
KJW
Well I just tossed –1 coins and only got half an outcome.
• September 7th, 2014, 03:07 PM
Robittybob1
Quote:

Originally Posted by Guitarist
Ya well, there is a slight problem here (in mathematical terms)

Suppose it is true that tossing coins, each with 2 possible outcomes gives a total of possible outcomes.

Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

Does it help to note that tossing coins just once has exactly the same number of possible outcomes as tossing a single coin times? Well, tossing a single coin zero times reveals the starting face, that is only outcomes.

How can you be sure you tossed the zero coins only once?
• September 7th, 2014, 03:38 PM
anticorncob28
Quote:

So zero coins tossed just once has 2^0 = 1 possible outcomes. Can this be true?
Yes. If there were zero outcomes of tossing zero coins, that would make it impossible to not flip zero coins. It would mean that no matter where you are or what you're doing, you would have to be flipping at least one coin.
• September 9th, 2014, 12:44 PM
TridentBlue
You also say "It can be written in smaller cases." Do you mean where you count HTT, THT, TTH (two tails one head) and as one outcome? If you want the formula with probability for that, you need the binomial distribution:

https://en.wikipedia.org/wiki/Binomial_distribution

If you toss 10 coins simultaneously, it will give the probability of each outcome (3 heads, 4 heads, etc)
• September 9th, 2014, 01:10 PM
GTCethos
Quote:

Originally Posted by Guitarist
Ya well, there is a slight problem here (in mathematical terms)

Suppose it is true that tossing coins, each with 2 possible outcomes gives a total of possible outcomes.

Now suppose I toss zero coins just once - don.t say this is not "physically possible", in mathematics this is irrelevant. So zero coins tossed just once has possible outcomes. Can this be true?

Does it help to note that tossing coins just once has exactly the same number of possible outcomes as tossing a single coin times? Well, tossing a single coin zero times reveals the starting face, that is only outcomes.

The simple answer is you are not talking a probability because…

Probable outcome is given (desired outcome / possible outcomes). You have no desired outcome only a possible outcome.
• September 9th, 2014, 01:44 PM
Dywyddyr
Quote:

Originally Posted by GTCethos
The simple answer is you are not talking a probability because…
Probable outcome is given (desired outcome / possible outcomes). You have no desired outcome only a possible outcome.

Arrant nonsense.
Probability has nothing whatsoever to do with "desired outcome".