if you buy one ticket everyday for 365 days and get a result of 1 winning tickets, is 1 a significantly low number of winning tickets? why or why not?

The solution for this problem is:

Cut wire so first piece has length x. 
Second piece has length (72 - x). 

Use piece of length x to make circle. 
c = circumference, r = radius 
c = 2πr = x 
r = x/(2π) 

A(circle) = πr² = π * (x/(2π))² = x²π/4π² = x²/4π 

Use piece of length (72-x) to make square. 
s = side length = (72-x)/4 

Area(square) = s² = ((72-x)/4)² = (72-x)²/16 = (5184 - 144x + x²)/16 
Area(square) = 324 – 9x + x²/16 

A = A(circle) + Area(square) 
A = x²/4π + 324 - 9x + x²/16 
A = x²/4π + x²/16 – 9x + 324 
A = 4x²/16π + πx²/16π - 9x + 324
A = (4+π)/16π x² - 9x + 324 

This is the function of a parabola that opens up. 

To look where A is minimum, you can rewrite equation in vertex form or find where derivative = 0. 

A' = 2(4+π)/16π x - 9 = (4+π)/8π x - 9 
A' = 0 
(4+π)/8π x - 9 = 0 
(4+π)/8π x = 9 
x = 9*8π / (4+π) 
x ≈ 31.7 inches