#------------------------------------------------------------------
# 	demere.py
#
#	Compute the probability of getting "double-six" at least
#	once during twenty-four throws of a pair of 'fair' dice. 
#
#		execute using:  $ python demere.py
#
# 	programmer: ALLAN CRUSE
# 	written on: 06 JAN 2011
#------------------------------------------------------------------

print "\n\n When tossing a pair of dice twenty-four times ... "
samples = 36 ** 24
print "\n size of the sample space: %d outcomes \n" % samples

failures = 35 ** 24
print " 'double-six' does NOT occur in %d cases \n" % failures

successes = samples - failures 
print " So odds in favor of getting 'double-six' at least once",
print "in twenty-four throws: "
print " %d:%d \n" % (successes, failures)

probability = 1.0 - (1.0 * failures)/(1.0 * samples)
print " Hence probability of getting 'double-six' at least once",
print "in 24 throws = %1.4f \n\n" % probability