ON PROBABILITY. - 
0 order 1 . . 
Ga 5 Since every one of the six numbers on one of the dice may combine with 
ho) 5 every one of the six on the other, the number of throws on the dice is 36, 
“allse the 
land 6 
0d 2hlart The number 7 may be made up of or 3 and 4), 
possi: or 2 and 5 
FAISe every and as these numbers may be on the one die or the other, there are in all 
“ES, I we six ways which favour the number 7, and therefore the probability required 
Der than a is 5; or 1. 
” Ex. 4. A, the dealer in a party at whist, desires to know the probability 
n both 18 of his partner holding a given card. The number of cards which are held 
with every by the other three players is 39 ; therefore the probability that the card in 
umber of question is any given cardin A’s partner’s hand is 44;, but it may be any one 
ida ble of the 13 cards which A’s partner holds, therefore the probability is 13 = 1. 
ada white Or thus, there are three cases possible: either the card is in the hand 
Le of A’s partner, or of one of the other two players; and as these three cases 
are similarly circumstanced, the probability of either of them is 2, the odds 
against it being of course 2 : 1. 
A desires to know the probability of his partner holding 2 given cards. 
The number of combinations of 39 things taken two and two together is 
39 x 38 -~ ) 
= therefore the probability that these two cards are any given two 
: 1 
cards in A’s partner's hand is 39 x 38 = -——————; but they may be any 
kn 30% 19 
bow 1.2 
teh two cards in A’s partner's hand ; therefore, since the number of combi- 
{0 the bag 
vw. 13 % 12 
nations of 13 cards taken two and two together, is ~13 = 15 w'@, 
13 x 6 2 : 
the probability required is oT es 19° the odds against are therefore 
17:2. , 
Similarly, the probability that he holds any three given cards, is 703 
the odds against are, therefore, 681 : 22. 
s event, Ex. 5. Reqnired the probability, that in a deal at whist each player 
ame, say J holds an honour. 
The number of permutations of 52 cards taken all together is 
or 52 x 51 . . . X 3 x 2 x 1, and the number of permutations of 13 cards 
= taken all together is 13 x 12 x11. . . . . . 3 X 2 X 1, therefore the 
(+2) & number of different deals is 
ar 577% BL G0 OE PEON Cuin w @ x] 
(4) ¥ Brix ; HY 
fan because the 13 cards may be permuted in each player's hand separately, 
(34) + without altering his hand. i 
The number of permutations of 48 cards taken all together is 
hd 48 x 47 x 46 . . . . . . 3 x 2 % 1, therefore the number of different 
- ways in which 48 cards can be dealt to four persons is 
= 48.5. 47. 9 40 tpi er to x 2 latin ani 3: 0.2.50: ] 
{12% HM x 10, Ree i 2 1)