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I'm getting a bit dumb on the probabilities. - page 7

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Mathemat:
No, they're not equivalent. You still have to group them into groups of four to see how many sixes there are.


In centurions, or legions, I'd understand. Why four of each?

I get it, I'm a bit of a klutz. Time for bed :)

Because the elementary event (the outcome of the test) is "at least one six in four rolls". I'm just going to throw out a programme.
Mathemat:
Because the elementary event (the outcome of the trial) is "falling at least one six in four rolls".

Surprise. It isn't.
[Deleted]
tara:

Svetlana, excuse me - we've been having a little chat with the namesake. What are you doing this morning?

You want to take me to the movies? :)
Swetten:
Do you want to invite me to a movie? :)

Yeah, for a cup of tea...
[Deleted]

Jackass. :)

Thank you :)

tara:

I'll surprise you. It isn't.
What about it?

Look here, namesake, this is a simulation of a game of maths (4 dice), a hundred million games:

#property show_inputs

extern int MAX = 32768;
extern int SERIES = 100000000;

int start( )
{
   int st = GetTickCount( );
   MathSrand( GetTickCount( ) );   
   
   int success = 0;
   for( int i = 0; i < SERIES; i ++ )
   {
      /// В этом маленьком цикле моделируется одна игра (бросок 4 костей). Как только получаем шестерку, игру прекращаем и записываем ее результат как "успех".
      for( int j = 0 ; j < 4; j ++ )
         if( genUniform( ) == 6 )          { success ++ ;   break; }

      ///if( i % 1000000 == 0 )        Comment( i / 1000000 + " mln." );
   }
   
   Print( "success rate = " + ( success + 0.0 ) / SERIES );
   int gone = ( GetTickCount( ) - st ) / 1000.0 ;
   Print( "Total time = " + gone + " sec." );
   return( 0 );
}//+------------------------------------------------------------------+


      int genUniform( )
      {
         int rand = MathRand( );
         return( 1 + 6 * rand / MAX );
      }//+------------------------------------------------------------------+

Result:


The simulation of a uniform distribution from 1 to 6 is not very accurate, but the error is small, no more than 0.001.

The S.Q. of the frequency deviation from the probability is MathSqrt( npq ) / n ~ 1/20000, so here too you have no chance of getting close to p=2/3.

The exact value of the probability (or...er...m.o. frequency) is 1 - (5/6)^4 ~ 0.517747.

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