Suppose the auction house from the preceding problem sold 200 tickets at $1 each, and had 16 prizes of $10 each. what is the new expected value?

a) $0
b) $0.2
c) –$0.2
d) $0.8

200/160=1.25

200+160=360/1.25/160=200.8

so your answer is 0.8

SymbolSymbol NameMeaning / definitionExample
xx variableunknown value to findwhen 2x = 4, then x = 2
≡equivalenceidentical to
≜equal by definitionequal by definition
:=equal by definitionequal by definition
~approximately equalweak approximation11 ~ 10
≈approximately equalapproximationsin(0.01) ≈ 0.01
∝proportional toproportional toy ∝ x when y = kx, k constant
∞lemniscateinfinity symbol
≪much less thanmuch less than1 ≪ 1000000
≫much greater thanmuch greater than1000000 ≫ 1
( )parenthesescalculate expression inside first2 * (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)*(1+5)] = 18
{ }bracesset
⌊x⌋floor bracketsrounds number to lower integer⌊4.3⌋= 4
⌈x⌉ceiling bracketsrounds number to upper integer⌈4.3⌉= 5
x!exclamation markfactorial4! = 1*2*3*4 = 24
| x |single vertical barabsolute value| -5 | = 5
f (x)function of xmaps values of x to f(x)f (x) = 3x+5
(f ∘g)function composition
(f∘g) (x) = f (g(x))
f (x)=3x,g(x)=x-1⇒(f ∘g)(x)=3(x-1)
(a,b)open interval(a,b) = {x | a < x < b}x ∈ (2,6)
[a,b]closed interval[a,b] = {x | a ≤ x ≤ b}x ∈ [2,6]
∆deltachange / difference∆t = t1 - t0
∆discriminantΔ = b2 - 4ac
∑sigmasummation - sum of all values in range of series∑ xi= x1+x2+...+xn
∑∑sigmadouble summation
∏capital piproduct - product of all values in range of series∏ xi=x1∙x2∙...∙xn
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞
γEuler-Mascheroni constantγ = 0.527721566...
φgolden ratiogolden ratio constant
πpi constantπ = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = π·d = 2·π·r