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126 to 1.

Questions on Cards and Lotteries.

213 reduce the expression to ta; this last spades, defires another to draw them may also be divided by 4; which re. one at a time; what are the odds of duces it to jão, so the probability is as that perion's drawing the hearts first,

and afterwards all the diamonds ?

Solution. The probability of taking Let there he given a nuziber of things, where

the hearts first is a ti, and that of of fore are several times repeated, for in- taking all the diamonds next, to i fance, A A, B B B, C C cc, &c. to collecting these together we have hind the probability, that hy drawing these ji to š, and multiplying as before, dette's or things represented by them one by one, they fali come out in the order here

we get ozoty, and dividing each part placed; that is, that all the A's fall come

by 12,

we reduce the expreflion to out firft, the B's next, &c.

zo žo, whence the odds are as 7920

3

1 i 2

to I.

LOTTERIES,

QUESTION 24.

(To be continued.) Suppose there are y counters, as before, but differently marked, for ex

CURIOUS QUESTIONS ON CARDS AND ample: let two of them be marked each A, three of them each B, and four of them each C; it is required to find the

(Continued from page 114.) probability that drawing them one by one, all the A's shall come out firit,

Examples calculated upon the 1987 Lottery, the B's next, and the C's the lait.

of the probability of Prizes against Blanka, Solution. There being 9 counters from three to twenty Tickets. in all, and two of them marked A, the probability of the A's coming out be. LET there be an Examples in the fore either a B, or a C, will be į š; ensuing, or any other Lottery, in which if this happens we have seven counters are 60,000 tickets, amongst which are left, viz. three marked B, and four 250 prizes of gol. each, what are the marked C, and the probability of draw- odds, that, in taking two tickets, I ing the B's next is o'}; wherefore hall have one prize of 50l. ? the probability of drawing the A's first, It being of no consequence to the soand the B's next, will be ó , and lution of this question, what other prizes multiplying, as before taught, we have there are in the Lottery, therefore all 13120, or by dividing each by 12, the rest of the tickets, except these 250 Tžov; so the probability of drawing may be esteemed as blanks. Now 250 the A's first, and the B's next, will be taken from 50,000, leaves 49,750,which as 1260 to 1.

If this happens, there is to be considered as the number of is no need of proceeding any farther, blanks in this queition; therefore, for the taking the Ç's next is a cer- te exprefies the probability of the tainty.

2 tickets being blanks or prizes under

gol.the upper product is 2,475,012,750, QUESTION 25.

the under one 2,499,950,000, their

difference 24,937,250, are the namber A certain person having 12 cards in of chances for having one prize, and the his hand, of which two are hearts, three required probability, as 2,499,950,000 Aiamonds, three clubs, and the rest to 24,937,250, or nearly as 1op to 1,

21

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A Table fhewing the probability of having one Prize out of any Lottery, upar

the Scheme of that of 1787.

Numb. 14.20,000. 10,000. 5,000.2,000.1,000.500.100.150. Above 20.

16244

1

14166

39
29
23
19
17
1416
13

62 25

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227 166

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206 115?

3 8333 to 1 5555 3333 1667

757 555 166 66 4

1 4166 2498 1249 568 416 125 50
5 14983 3333 1998 999

455 333 100 40
6
1 2778 1666

833 379 277 83 33
7 3571 1 2381 1428 714 325 238 71 28
8
13122
12083 1249 625

284 208
9 12778 1852 10 556 252 185 55 22
IO 2491

1666

999 500 II 2273

1515 909 455 I 2

12083 1389 833 416 | 189 139.41 16 13 1923

1282
769 | 385 175

3815
14
1786
1190 714 357

162

119 35 | 14
15
11666
IIIO 666

333
151 III

33 13
16 1562

1041 625 317 142 104 17 1470 980 588

294 133

98 29 18 1389 I

555

92 27 191316 877 526263

87 26 101
1245
499 250 113

83

25

50 20 45 ) 18

I

1018
10
9

I

128

I

816

1

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The Use of the preceding Table. red, I am required to draw 2, and in

case one of the two be a red one, I am The first column contains the num- to receive the sum of 5 shillings, what ber tickets, the rest of the columns con

is the value of my expectation ? tain odds against having any respective Solution. Find as before the proprize, specified at the top of the table : bability of drawing tivo black counters for instance, suppose I purchase 6 tic- fuccesively thus: the probability of kets in the ensuing state lottery, I defire drawing a black counter the first time to know the probability of my having will be as 10 to 7, that of taking a black one of these tickets a roool. prize? I one the second time as oto 6, or as 3 look in the first column, under Numb.

2, because both the 9 and the 6 may be for 6, and against it, under 1000, I reduced to lower quantities, they being find 379, by which I see that it is 379. both divisible by 3; then collecting to i that I have a 1000l. prize out of these two probabilities together, we have the 6 tickets.

1 }; the product of 10 by 3 is 30, Again, suppose I purchase 12 tickets, and that of by 2 is 14 ; therefore, the what are the odds against me, that I probability of drawing tivo black coun, hive one prize of gol.? I look for 12

ters successively is as 30 to 14, that is, in the firit column, and against it in a

as 15 to 7, becaule 30 and 14 may both right line under 50, I find 16, which be divided by 2;

now 7, the number thews that it is as 16 to i that I have a

of chances for drawing two blacks frize of gol. out of the 12 tickets.

counters fucceflively, being taken from

15, the whole number of chances, leaves To find the Value of a Person's Expectation

8 for the number of chances for taking on any particular Chance,

one white counter, so the required proQUESTION 12.

bability is as 15 to 8; now to find the

value of the expectation, there being 15 Suprose that out of a heap of 10 chances in the whole, 8 of which are in counters, of which

7
are black and
3 my favour, therefore, the value of my

expectatica

The Wag's Trick, concluded.

215 expectation will be found by dividing odds that one of the three shall be an 5 Thillings into 15 parts, and taking 8 ace? of those parts, I shall have the value re- The probability that the first card quired; thus in 5 hhillings are 60

pence,

drawn shall not be an ace is 13 to 12, which divided by 15, quotes 4, and this or i}; that of the second not being an multiplied b; 8, gives 32 pence, or two ace as 12 i0 il, or íí; and that of the fhillings and eight-pence. Or the ge- third not being an ace as 11 to 10, or

ral method is to multiply the suin by fi, and the total of these probabilities the number of chances in your favour, will be } ki, the product of the and that product, divided by the whole lower numbers is 1716, and that of the number of chances, gives the value ; upper ones 1320 ; therefore the prothus 5 shillings multiplied by 8, gives bability of the three cards being neither 40, and this divided by 15, quotes 2

of them an ace ii 26 1716 to 1320 ; fillings and 8 pence, the same as before. their difference 396 are the number of

chances for one of the said three cards QUESTION 13

being an ace; to the odds are as 1716

to 396, or as 13 to 3. There are two parcels of three cards

(To be continued.) each, the first containing king, queen, and knave of hearts, the second parcel the king, queen, and knave of diamonds : now suppose I am proinised DROLL TRICK WITH A COCK. the suin of 3 guincas, in case that in taking a card out of each parcel, I shall

(Concluded from Page 145.) take either the king of hearts or the king HALF a crown was the price for feeof diamonds, required the value of mying this great curiosity; and to make it expectation!

appear as not a mere take in, no money Solution. The probability of not was to be received till after the pertaking a king from the first parcel, is as formance. 3 to 2, and that of not taking a king Bills in writing were likewise distrifrom the other parcel likewise as 3 to 2, buted, and not a few attended at the because they being separate parcels, the inn; the scholars laughed in their drawing a card from one, does not at fleeves; they had heard and seen the all affect the drawing of one from the Jonas's, the Comas's, the Breslaw's, and other, therefore the numbers continue the Katerfelto’s; but this trick promised the same in both probabilities, and are to surpass thein all.

}, their products give 4 and 9, and In the mean time a fowl was laid their difference 5 are the number of down to the fire, and the cook brought chances for taking a king from one of into the confederacy; a large bason of the parcels, and the probability as 9 to egg fauce was made, and left to cool, 5: The value of the cxpectation is the cloth was laid, and the guests dethus found: in 3 guineas are 63 shil- fired to walk in ; the needy contriver lings; then multiply 63 by 5, and di- of the scheme was as busy as could be, vide the product by 9, gives 35 fhil. entertaining the company with a mullings, the value required ; to that if a titude of extraordinary fiories to divert person was to purchase my chance, he their attention, while he carried on the ought to give me one pound fifteen Thil. deception; at last the foirl was done, lings for it.

several were present at its being taken

off the spit, and then haftened into the QUESTION 14.

parlour; mean time another dish was

ready close to the door, with the live Suppose that out of a suit of 13 cards, fowl stripped of its feathers in it, and three cards be drawn, what are the covered over with the cold eos fauce.

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on.

As soon as this was set upon the table To tell what card a person thinks opon, though (far the change was managed so clearly,

you are not in the rooin, or which card he

has touched, or waved nis hand over, that no person perceived it), one of the ftudents ítuck in his fork, with a degree

TO do this trick you muit lay a of vehemence, that made the fowl

qu!t its supineness, run from the dish, and wager that you will icll the card the fiuttering its wings, befpattered the fee it ; let several cards be laid out on

perfin hus touched, though you do not company all over with egg fauce; and actually made off with the fork, to the ber, then turn your back, or leave

a table, 1, 2, 3, 4, 5, 6, or any mimno small surprise and inirth of the be- the room while the person makes choice; holders, The man having thus fulfilled his he will lay, having your eye upon the

on your return, you must enquire what promise, began to collect the half- cards laid out; it he lays he will lay Crowns, which umbled in pretty pien, fix to ore, or ten to one, you must take tifully; the real roatted fou l was served the higheit number, as that will, in all in with other provisions; and after fupi probability, be the card he had fixed per, the evening was concluded wiih

You must seem to pause about che utmost barınony, and much to the fatisfaction of the wag, who was the counting the cards as they lay, and

choofing the farthelt off. contriver, and u hofilled his pockets by de experiment.

To call for any card in the pack. For a person to chure a card, you not fiprosei

THIS trick, which requires very lits to know what it is, and inen for the per. tle practice, or indeed understanding, to fon to hold the cards between luis te ger perform, is done in the following manand thurih, to strike them all out of his hand except the very card fie had tak, 11.

Having privately seen a card, put it

at the bottom of the pack, then shuffle THIS is calleů the Nerve trick, and the cards till it comes to the botton is thus performed: having previously again, then put the cards behind you ; looked at a card, bid the person draw and fay here I call for, naming the botone, taking care to shove that to which tom card, which you have seen; and you know; when he has looked at it, as you hold them behind you, turn the let him put it at the bottom; let him top card with its face upwards, then inu file the cards, then you look at them hold forth the cards, and as you hold again, and finding the card, place it at them you may see what the next card the bottom; then cut them in half; is; then put the cards behind you again, give the party that part which contains and take the top card, and put it at the his chosen card at the bottom, to look bottom, with its face downwards, and between his finger and thumb juit at turn the next card with its face upthe corner ; bid him pinch thcin as wards, and whilst you are doing this, right as he can ; then striking them pret- say, here I call for, naming the card you ty Tharp, they will all fil to the ground faw laft; then hold forth the cards again, except the bottom one, which is the thewing the botton card, which wil be card he had chosen.

that

you call for ; then put the cards beThis is a very curious trick, and if hind you again, and proceed in the same cleanly done, is really attonithing; but manner as you did before; you may by may be accounted for from the nature this method go through thein all, and of the nerves, which are always more call for all the cards in the pack, to the retentive when any thing is attempted admiration of the beholders, who will be 10 be tiken either by force or fur- furprised how you could find them out, prizę.

whin you hold thein out behind you.

ner:

( 217 )

ALBERTUS'S SECRETS OF NATURE.

(Continued fro:n Page 199.)

TO make the fruit of the citron-tree fire thereto, and the experiment will fall off: to five parts of citron-colour verify what has been faid upon it. fulphur, five of black, and two of white, That a candle may seem self-motive let there be added some vermilion, when lighted: take cqual parts of tie with which fumigate the tree, and its skins of a wolf and a dog, which, formfruit will fall of; the same eifcct will ed into the shape of a candle, bełmear perhaps follow the application of the with oil of olives, and it will, to all apabove composition to other trees. pearance, immediately begin to move.

How to kill a fe pentin tantaneously: Take a piece of new white cloth, and take a quantity of Aristol chy, pound it having wrapped in it a serpent's eat, well, with which mingle the powder of dip it in olive oil, which, give to any a frog pulverized, adding thereto a lit- bye ftander to light, and he will be tle varnish, which done, write there- tray manifest tokens of fear, trembling with on a piece of paper, and throw it all the time it continues in his hand. to the serpents.

The forehead, in the opinion of phi. To make a house or chamber appcar losophers, for its structure, is reckoned full of ferpents: take the fat of a fer- the principal in that part of the human pent, and some salt, divide it into four frame. Soon after death, in this part equal parts, putting one into each of are generated worms, which, in the four pieces of a funeral pall, which, space of seven days, assume the aphaving twisted into the form of a call- pearance of flies; in fourteen days thcy dlewick, dip in oil (of elder---these become venemous creatures, whose bitc being lighted, will produce the above is mortal : Take a part of the human extraordinary appearance,

fleth that has fuifered by their virulence, Conception is said to be accelerated few it with oil, and the candie thence

a woman's having about her in the formed being lighted, shapes will dil-") act of coition some powdered hartíhorn, cover themselves, which, to look upon, mingled with cow's gall.

will excite inexprellible horror. Camphor, it is supposed, when laid The rcsult of experiments creates aon the water will take fire and burn.

mazement, which ceases upon a thoTo make an artificial topaz : take, ac- rough investigation of the causes, and cording to the fize you intend, the an insight into the nature of the agent whites of hens eggs, anoint them with and patient, the aptitude of cach to prosaffron, and, in the space of a month, duce the effect which occafions wouthey will exhibit a vitrification equal in der. When we see cold water kindle hardness to stone.

fire in Atead of impeding its progress to An abhorrence from wine may be a flame, by attending only to the agent, created by giving a person to drink of we cannoi help being surprised; buc that liquor, wherein eels had died. when it is considered that the matter

A method of making a wick, which, which aids the effect, quick lime or when set fire to, will produce in an 3- sulphur, for initance, are in their napartment the appearance of birds, Ay- tures extremely infiammable, so that ing to and fro : take a new pall or the smalleit cifort is sufficient to make fhrowd, in it wrap the brain of a bird, them glow into flame, the prodigy is and the feathers of his tail, which roll at an end. In like manner, when we into the form of a wick, and put into a see any thing consumed by fire, the new green lamp: the oil to be made phenomenon seems extraordinary, as use of on this occasion is olive cil; {et long as only one of the causes concern

ing

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