Devise a fair scheme for eliminating coins in this country.
Here is an alternative question:
Michael Rossides has come up with a scheme for eliminating
coins. This scheme involves probability and the fact that
most cash registers today are computers. Suppose that
every cash register could be programmed with a random
number generator; that is, suppose that it were possible
to pick a random number from 1 to 99. Rossides' system
works as follows. Suppose you purchase items totaling
$15.89. The computer would choose a number from 1 to 99
and then compare it with the cents portion of the purchase.
In this case, if the random number is between 1 and 89
the price would be rounded up to $16; if it is between
90 and 99 the price would be rounded down to $15. For
example, if you purchase a cup of coffee for $1.20, and
the random number generator produces a random number from
1 to 20, the price is $2, but if it produces a number
from 21 to 99 the price is $1. Write a paper commenting
on this scheme.
Find the probability that the 13th day of a randomly
chosen month will be a Friday. (Hint: It is not correct
to say that the probability is 1/7 because there are seven
possible days in the week. In fact, it turns out that
the 13th day of a month is more likely a Friday than any
other day of the week.) Write a paper discussing this
problem.
References:
William Bailey, "Friday-the-Thirteenth," The Mathematics
Teacher, Vol. LXII, No. 5 (1969), pp. 363-364.
C. V. Heuer, Solution to Problem E1541 in American
Mathematical Monthly, Vol. 70, No. 7 (1963), p. 759.
G. L. Ritter, et al, "An Aid to the Superstitious,"
The Mathematics Teacher, Vol. 70, No. 5 (1977),
pp. 456-457.
