Mathematical_Recreations-Kraitchik-2e

Probabilities
l~l
one suit will not be represented, that is, that the hand will be
blank in one suit. Similarly, one may find the probability of
having at least one singleton, or of having a 9-card suit. The
next table lists the probabilities that some suit will be represented
in the hand by just n cards.
Cards in sui t Probability Cards in sui t Probability
0 0.0510 4 0.3508
1 .3055 5 .4434
2 .5381 6 .1655
3 .1054 7 .0354
8 .0047
9-13 .0002
1.0000 1.0000
Here is a table telling what hopes one may have of finding
trumps in the dummy:
Trumps
in bid-
Probability of the occurrence in the dummy
of just n trumps
Total
der's
hand n= In = 2 n=3 n=4 n=5 n=6 n = 7 n=8
--------------
4 - - - .2219 .0908 .0211 .0027 .0001 0.3366
5 - - .3057 .1738 .0544 .0091 .0007 .0000 0.5437
6 - .3336 .2355 .1024 .0230 .0025 .0001 - 0.6971
7 .2621 .3574 .2279 .0712 .0103 .0005 - - 0.9294
4. THE ERROR CURVE. In many applications of probabilities
one must use the error curve (Figure 19), whose equation
is y = Ae-bZ'. This curve may be thought of as arising
in the following way. Suppose an experimenter has to measure
a certain quantity. He is able to read off measurements
from his instrument to within a certain degree of accuracy,
say 0.0001 inch. Successive measurements of the same quantity
will not ordinarily produce the same readings. If he