**1.**Let the bottom edge of a rectangular mirror on a vertical wall be parallel to and

*h*feet above the level floor. If a person with eyes

*t*feet above the floor is standing erect at a distance

*d*feet from the mirror, what is the relationship among

*h*,

*d*, and

*t*if the person can just see his own feet in the mirror?

(A) $$t=2h$$ and $$d$$ does not matter.

(B)

*t=4d*and

*h*does not matter.

(С) $$h^2+d^2=\frac {t^2}4.$$

(D)

*t-h=d*.

(E) $$(t-h)^2=4d.$$

**2.**Let

*A*and

*B*be subsets of a set

*M*and let $$S_0=\{A,B\}$$. For $$i\ge0$$, define $$S_{i+1}$$ inductively to be the collection of subsets

*X*of

*M*that are of the form $$C\cup D, C\cap D$$, or $$M-C$$ (the complement of

*C*in

*M*), where $$C,D\in S_i$$. Let $$S=\bigcup_{i=0}^\infty S_i$$. What is the largest possible number of elements of

*S*?

**3.**A fair die is tossed 360 times. The probability that a six comes up on 70 or more of the tosses is

(A) greater than 0.50

(B) between 0.16 and 0.50

(C) between 0.02 and 0.16

(D) between 0.01 and 0.02

(E) less than 0.01