Generalize De Moivre’s procedure in Problem III (of this text) to solve Problem IV: To find how many...

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Generalize De Moivre’s procedure in Problem III (of this text) to solve Problem IV: To find how many trials are necessary to make it equally probable that an even willhappen twice, supposing that a is the number of chances for its happening in any one trial and b the number of chances for its failing. (Hint: Note that is the number of chances in which the event may succeed no more than once, while ()is the total number of chances. Approximate the solution for the case where a:b=1:q, with q large, and show that 1.678q.
	
Document Preview: Generalize De Moivre’s procedure in Problem III (of this text) to solve Problem IV: To 
find how many trials are necessary to make it equally probable that an even will 
happen twice, supposing that a is the number of chances for its happening in any one 
    
trial and b the number of chances for its failing. (Hint: Note that       is the 
 
( )
number of chances in which the event may succeed no more than once, while     is 
the total number of chances. Approximate the solution for the case where a:b=1:q, with 
q large, and show that    1.678q.

David · Accepted Answer

Sol:  
          Let the number of chances for its happening in any one trial be ,a and the 
number of chances for its failing be ;b and the number of trails is .x From the hint, xb
will represent the number of chances of the event’s failing x times successively, 
1x xb xab  is the number of chances whereby the event may fail,

Generalize De Moivre’s procedure in Problem III (of this text) to solve Problem IV: To find how many trials are necessary to make it equally probable that an even willhappen twice, supposing that a is...

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