The Sock Drawer Problem¶
Problem 1 from Fifty Challenging Problems in Probability by Frederick Mosteller¶
"A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is $\frac{1}{2}$. (a) How small can the number of socks in the drawer be? (b) How small if the number of black socks is even?"
In [1]:
# Initialize with 2 red socks and 1 black sock.
Red=2
Black=1
# define a tolerance factor
tol=1e-5
# Drawer Capacity (limits the search space)
cap=100
def prDraw2Red(r,b):
'''
Function returns the prob of drawing two red socks.
args: (num red socks, num black socks)
'''
pr1=float(r)/(r+b) # probability first sock drawn out is red
pr2=float(r-1)/((r-1)+b) # probability second sock is red, given first was red
return pr1*pr2 # probability both red
P=prDraw2Red(Red,Black)
Total=Red+Black
while abs(P-0.5)>tol and Total<cap:
if P < 0.5:
Red+=1
else:
Black+=1
P=prDraw2Red(Red,Black)
Total=Red+Black
print " Red =", Red, " Black =", Black, " Prob =", P, " Total Socks =", Total
