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Questions on Cards and Lotteries.

4

reduce the expreffion to this laft may also be divided by 4, which reduces it to fo the probability is as

126 to I.

1269

213

fpades, defires another to draw them one at a time; what are the odds of that perion's drawing the hearts firft, and afterwards all the diamonds?

2 3

1

Solution. The probability of taking the hearts firft is, and that of Let there be given a number of things, whereof fore are feveral times repeated, for in- taking all the diamonds next, ; ftance, A A, B B B, C C C C, &c. to collecting thefe together we have iz find the probability, that by drawing thefe, and multiplying as before, letters or things reprefented by them one by we get, and dividing each part one, they hall come out in the order here by 12, we reduce the expreflion to 70, whence the odds are as 7920

placed; that is, that all the A's fhall come out firft, the B's next, &c.

QUESTION 24.

Suppofe there are 9 counters, as before, but differently marked, for example: 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 probability that drawing them one by one, all the A's fhall come out first, the B's next, and the C's the last.

Solution. There being 9 counters in all, and two of them marked A, the probability of the A's coming out before either a B, or a C, will be; if this happens we have feven counters left, viz. three marked B, and four marked C, and the probability of drawing the B's next is; wherefore the probability of drawing the A's first, and the B's next, will be 3, and multiplying, as before taught, we have TSIZ, or by dividing each by 12, To fo the probability of drawing the A's first, and the B's next, will be as 1260 to 1. If this happens, there is no need of proceeding any farther, for the taking the C's next is a certainty.

12

QUESTION 25.

21 2

A certain perfon having 12 cards in his hand, of which two are hearts, three diamonds, three clubs, and the rest

to I.

(To be continued.)

CURIOUS QUESTIONS ON CARDS AND LOTTERIES.

(Continued from page 114.)

Examples calculated upon the 1787 Lottery, of the probability of Prizes against Blanks, from three to twenty Tickets.

LET there be an Examples in the enfuing, or any other Lottery, in which are 60,000 tickets, amongit which are 250 prizes of 50l. each, what are the odds, that, in taking two tickets, I fhall have one prize of 50l.?

It being of no confequence to the folution of this question, what other prizes there are in the Lottery, therefore all the rest of the tickets, except these 250 may be efteemed as blanks. Now 250 taken from 50,000, leaves 49,750,which is to be confidered as the number of blanks in this question; therefore 750, 4923 expreffes the probability of the 2 tickets being blanks or prizes under gol.the upper product is 2,475,012,750, the under one 2,499,950,000, their difference 24,937,250, are the number of chances for having one prize, and the required probability, as 2,499,950,000 to 24,937,250, or nearly as 109 to 1.

4974

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A Table fhewing the probability of having one Prize out of any Lottery, upon the Scheme of that of 1787.

Numb. 4.20,000. 10,000. (5,000. 2,000. 1,000.500. | 100.50. Above 201.

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The Ufe of the preceding Table.

The first column contains the number tickets, the reft of the columns contain odds against having any refpective prize, fpecified at the top of the table : for inftance, fuppofe I purchase 6 tickets in the enfuing ftate lottery, I defire to know the probability of my having one of these tickets a 1000l. prize? I look in the firft column, under Numb. for 6, and against it, under 1000, I find 379, by which I fee that it is 379 to I that I have a 1000l. prize out of

the 6 tickets.

Again, fuppofe I purchafe 12 tickets, what are the odds against me, that I have one prize of 50l.? I look for 12 in the first column, and againft it in a right line under 50, I find 16, which fhews that it is as 16 to 1 that I have a prize of 5ol. out of the 12 tickets.

To find the Value of a Perfon's Expectation on any particular Chance,

QUESTION 12.

Suprofe that out of a heap of 10 Counters, of which 7 are black and 3

119 87 26 10

83 25

am

red, I am required to draw 2, and in cafe one of the two be a red one, I a to receive the fum of 5 fhillings, what is the value of my expectation?

Solution. Find as before the probability of drawing two black counters fuccefively thus: the probability of drawing a black counter the first time will be as 10 to 7, that of taking a black one the fecond time as 9 to 6, or as 3 to 2, because both the 9 and the 6 may be reduced to lower quantities, they being both divifible by 3; then collecting thefe two probabilities together, we have

14,

that is,

the product of 10 by 3 is 30, and that of 7 by 2 is 14; therefore, the probability of drawing two black coun ters fucceffively is as 30 to as 15 to 7, becaufe 30 and 14 may both be divided by 2; now 7, the number of chances for drawing two blacks counters fucceffively, being taken from, 15, the whole number of chances, leaves 8 for the number of chances for taking one white counter, fo the required probability is as 15 to 8; now to find the value of the expectation, there being 15 chances in the whole, 8 of which are in my favour, therefore, the value of my expectation

The Wag's Trick, concluded.

215

odds that one of the three shall be an ace?

The probability that the firft card drawn fhall not be an ace is 13 to 12, or 1; that of the fecond not being an ace as 12 to 11, or; and that of the third not being an ace as 11 to 10, or

expectation will be found by dividing 5 fhillings into 15 parts, and taking 8 of thofe parts, I fhall have the value required; thus in 5 fhillings are 60 pence, which divided by 15, quotes 4, and this multiplied by 8, gives 32 pence, or two fhillings and eight-pence. Or the general method is to multiply the fum by, and the total of thefe probabilities the number of chances in your favour, and that product, divided by the whole number of chances, gives the value ; thus 5 fhillings multiplied by 8, gives 40, and this divided by 15, quotes 2 fhillings and 8 pence, the fame as before.

QUESTION 13.

There are two parcels of three cards each, the first containing king, queen, and knave of hearts, the fecond parcel the king, queen, and knave of diamonds now fuppofe I am promised the fum of 3 guineas, in cafe that in taking a card out of each parcel, I fhall take either the king of hearts or the king of diamonds, required the value of my expectation

Solution. The probability of not taking a king from the first parcel, is as 3 to 2, and that of not taking a king from the other parcel likewife as 3 to 2, because they being feparate parcels, the drawing a card from one, does not at all affect the drawing of one from the other, therefore the numbers continue the fame in both probabilities, and are

2 2

, their products give 4 and 9, and their difference 5 are the number of chances for taking a king from one of the parcels, and the probability as 9 to 5. The value of the expectation is thus found in 3 guineas are 63 fhil lings; then multiply 63 by 5, and divide the product by 9, gives 35 fhillings, the value required; fo that if a perfon was to purchase my chance, he ought to give me one pound fifteen fhil lings for it.

QUESTION 14.

Suppofe that out of a fuit of 13 cards, three cards be drawn, what are the

will be 1, the product of the lower numbers is 1716, and that of the upper ones 1320; therefore the probability of the three cards being neither of them an ace is as 1716 to 1320; their difference 396 are the number of chances for one of the faid three cards being an ace; fo the odds are as 1716 to 396, or as 13 to 3.

(To be continued.)

DROLL TRICK WITH A COCK.

(Concluded from Page 145.)

HALF a crown was the price for feeing this great curiofity; and to make it appear as not a mere take in, no money was to be received till after the performance.

Bills in writing were likewife diftributed, and not a few attended at the inn; the fcholars laughed in their fleeves; they had heard and feen the Jonas's, the Comas's, the Breflaw's, and the Katerfelto's; but this trick promifed to furpafs them all.

In the mean time a fowl was laid down to the fire, and the cook brought into the confederacy; a large bafon of egg fauce was made, and left to cool, the cloth was laid, and the guests defired to walk in; the needy contriver of the fcheme was as bufy as could be, entertaining the company with a multitude of extraordinary fiories to divert their attention, while he carried on the deception; at laft the fowl was done, feveral were prefent at its being taken off the fpit, and then haftened into the parlour; mean time another difh was ready clofe to the door, with the live fowl ftripped of its feathers in it, and covered over with the cold egg fauce.

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As foon as this was fet upon the table (for the change was managed fo cleanly, that no perfon perceived it), one of the ftudents tuck in his fork, with a degree of vehemence, that made the fowl quit its fupineness, run from the difh, and fluttering its wings, befpattered the company all over with egg fauce; and actually made off with the fork, to the no fmall furprife and mirth of the beholders.

The man having thus fulfilled his promife, began to collect the halfcrowns, which tunabled in pretty pientifully; the real roatted fowl was ferved in with other provifions; and after fupper, the evening was concluded with the utmost barmony, and much to the fatisfaction of the wag, who was the contriver, and who filled his pockets by the experiment.

For a perfon to chufe a card, you not fuppofed to know what it is, and then for the per fon to hold the cards between his fi ger and thumb, to flrike them all out of his hand except the very card he had tak、n.

THIS is called the Nerve trick, and is thus performed: having previously looked at a card, bid the perfon draw one, taking care to fhove that to which you know; when he has looked at it, let him put it at the bottom; let him fhuffle the cards, then you look at them again, and finding the card, place it at the bottom; then cut them in half; give the party that part which contains his chofen card at the bottom, to look between his finger and thumb just at the corner; bid him pinch them as tight as he can; then ftriking them pretty fharp, they will all fall to the ground except the bottom one, which is the card he had chofen.

This is a very curious trick, and if cleanly done, is really aftonifhing; but may be accounted for from the nature of the nerves, which are always more retentive when any thing is attempted to be taken either by force or fur prizę.

To tell what card a perfon thinks upon, though you are not in the room, or which card he has touched, or waved his hand over.

TO do this trick you must lay a wager that you will tell the card the perfon has touched, though you do not fee it; let feveral cards be laid out on a table, 1, 2, 3, 4, 5, 6, or any number, then turn your back, or leave. the room while the perfon makes choice; he will lay, having your eye upon the on your return, you muit enquire what cards laid out; if he fays he will lay fix to one, or ten to one, you must take the highest number, as that will, in all probability, be the card he had fixed

on.

You must feem to pause about counting the cards as they lay, and choofing the fartheft off.

To call for any card in the pack.

THIS trick, which requires very lits tle practice, or indeed underftanding, to perform, is done in the following man

ner:

Having privately feen a card, put it at the bottom of the pack, then fhuffle the cards till it comes to the bottom again, then put the cards behind you; and fay here I call for, raming the bottom card, which you have feen; and as you hold them behind you, turn the top card with its face upwards, then hold forth the cards, and as you hold them you may fee what the next card is; then put the cards behind you again, and take the top card, and put it at the bottom, with its face downwards, and turn the next card with its face upwards, and whilft you are doing this, fay, here I call for, naming the card you faw laft; then hold forth the cards again, fhewing the bottom card, which wil be that you call for; then put the cards be-. hind you again, and proceed in the fame manner as you did before; you may by this method go through them all, and call for all the cards in the pack, to the admiration of the beholders, who will be furprifed how you could find them out, when you hold them out behind you.'

( 217 )

ALBERTUS'S SECRETS OF NATURE.

(Continued from Page 189.)

TO make the fruit of the citron-tree fall off to five parts of citron-colour fulphur, five of black, and two of white, let there be added fome vermilion, with which fumigate the tree, and its fruit will fall of; the fame effect will perhaps follow the application of the above compofition to other trees.

How to kill a ferpent instantaneously: take a quantity of Ariftolechy, pound it well, with which mingle the powder of a frog pulverized, adding thereto a little varnish, which done, write therewith on a piece of paper, and throw it to the ferpents.

To make a house or chamber appear full of ferpents: take the fat of a ferpent, and fome falt, divide it into four equal parts, putting one into each of four pieces of a funeral pall, which, having twifted into the form of a candlewick, dip in oil of elder-thefe being lighted, will produce the above extraordinary appearance.

Conception is faid to be accelerated a woman's having about her in the act of coition fome powdered hartfhorn, mingled with cow's gall.

Camphor, it is fuppofed, when laid on the water will take fire and burn.

To make an artificial topaz: take, according to the fize you intend, the whites of hens eggs, anoint them with faffron, and, in the space of a month, they will exhibit a vitrification equal in hardness to stone.

An abhorrence from wine may be created by giving a perfon to drink of that liquor, wherein eels had died.

fire thereto, and the experiment will verify what has been faid upon it.

That a candle may feem felf-motive when lighted: take equal parts of the fkins of a wolf and a dog, which, forme ed into the fhape of a candle, befmear with oil of olives, and it will, to all appearance, immediately begin to move.

Take a piece of new white cloth, and having wrapped in it a ferpent's car, dip it in olive oil, which, give to any bye ftander to light, and he will betray manifeft tokens of fear, trembling all the time it continues in his hand.

The forchead, in the opinion of philofophers, for its structure, is reckoned the principal in that part of the human frame. Soon after death, in this part are generated worms, which, in the fpace of feven days, affume the appearance of flies; in fourteen days they become venemous creatures, whofe bite is mortal: Take a part of the human fleth that has fuffered by their virulence, flew it with oil, and the candle thence formed being lighted, fhapes will dif-✨ cover themfelves, which, to look upon, will excite inexpreflible horror.

The refult of experiments creates amazement, which ceases upon a thorough inveftigation of the caufes, and an infight into the nature of the agent and patient, the aptitude of cach to produce the effect which occafions wouder. When we fee cold water kindle ... fire instead of impeding its progress to a flame, by attending only to the agent, we cannot help being furprifed; but when it is confidered that the matter which aids the effect, quick lime or fulphur, for instance, are in their natures extremely inflammable, so that the fmallest effort is fufficient to make them glow into flame, the prodigy is at an end. In like manner, when we fee any thing confumed by fire, the phenomenon feems extraordinary, as long as only one of the caufes concern

A method of making a wick, which, when fet fire to, will produce in an apartment the appearance of birds, flying to and fro: take a new pall or fhrowd, in it wrap the brain of a bird, and the feathers of his tail, which roll into the form of a wick, and put into a new green lamp: the oil to be made ufe of on this occafion is olive cil; fet

ing

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