( 68o )

'The Meihod os Finding this Answer beingsomewhatoutoftheCommonRoad, I (hall here Add it; and thereby Infinite Solutions of the fame ksndmay be Discovered.

I st. Lottery, 2 i. Lottery.

Let <* — the Number of BUnks. m — the Number of Blanksl

b — the Number of Prtzes. n =: the Number of Prizes.

'7 — the Value of a Prize. t = the Value of a Prize.

i = to what you pay for a Lot ; viz. a Shiüing.

So the Lottery has its Chances for i ,and the Gamester his for r—r. NowtheTrueO<&& consisting of the Compounded Proportion of the Chances and

the Values\ viz. j and — the Sbare of the Lottery will be a, and that

of the Gamester rb — b. Therefore as the present case stands, the FirstLottery must be, «r—zr^- Z^; and by the likeReasoning the Stcond Lot-tery will be 2 n. Now the Value of a Lot beingthe Sum of the

Triz.es Divided by the Number of Lots, (which must be Equal in both Let-r b sn

teries) it yiclds

m

So to proceed.

■aV

b

m >- ?n

A-irh — ibm— 2 sn — 2 nrb sn

a+-b

(*)

C)

C)

m +- n

Let

'b

= 9

7 * * +- 8

8x39

1 4-3^109, IO II

Scope4 t, 1213-^3^14

12, 14

ScopeU, 1617 : 3«16, 18

1 6

17

18

*-r-brb=zqa-t-qb

3rb = z<ya+- 3 qb

3 rb — a-b- 3 b

%qa 4 - sqb=za+- 3 b

If a = o, to avoid Negative Numbers7 - 1

q P' r, malte- L ; q •<£ 1, makcs ap? o

in = o ,

i q a = a7 = ?

q ^ t, makcs b 05 qp? j,rcakes bp? o

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