C 405 ] 
Let us then firft fuppofe, of fuch an event as that 
called M in the effay, or an event about the proba- 
bility of which, antecedently to trials, we know no- 
thing, that it has happened once, and that it is en- 
quired what conclufion we may draw from hence 
with lefpedt to the probability of it’s happening on a 
fecond trial. 
The anfwer is that there would be an odds of three 
to one for fomewhat more than an even chance that 
it would happen on a fecond trial. 
For in this cafe, and in all others where q is 
nothing, the expreffion n -\- 1 x f 1 x ^^ 1 
/>+i p-\~i P + 1 P + ~ l 
or A — x gives the folution, as will appear 
fiom confi derin g the f rft rule. Put therefore in this 
expi efiion p + x ~ 2, X = 1 and x = JL and it will be 
1 01 * -I y which fhews the chance there is that 
the probability of an event that has happened once 
lies fomewhere between 1 and i.; or (which is the 
fame) ^the odds that it is fomewhat more than an 
even cnance that it will happen on a fecond trial 
In the fame manner it will appear that if the event 
has happened twice, the odds now mentioned will be 
feven to one 5 if thrice, fifteen to one 5 and in gene- 
ral, if the event has happened p times, there will be 
an odds of 2^ + 1 — 1 to one, for more than an equal 
chance that it will happen on further trials. 
Again, fuppofe all I know of an event to be that 
it has happened ten times without failing, and the 
, . Th ere can *' fuppofe, be no reafon for obferving that on 
tms fubjedt unity is always made to ftand for certainty, and ~ 
for an even chance, 
Voi. LIII. G g g enquiry 
