Download Formula Sheet for the Final

Useful definitions and facts:
• For any sets A and B,
n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
• For any event E
P (E) =
n(E)
.
n(S)
• For any event E, F ,
P (A ∪ B) = P (A) + P (B) − P (A ∩ B).
• P (E c ) = 1 − P (E)
• P (E) = 1 − P (E c )
• For two events E, F
P (E | F ) =
P (E ∩ F )
P (F )
• Product Rule With P (E) > 0, P (F ) > 0, then
P (E ∩ F ) = P (F )P (E | F ) = P (E)P (F | E).
• Permutations
P (n, r) =
n!
.
(n − r)!
• Combinations
C(n, r) =
n!
.
r!(n − r)!
• Number of Distinguishable Permutations
n!
n1 !n2 ! · · · nk !
• EX = µ = x1 p1 + · · · + xn pn and Var(X) = (x1 − µ)2 p1 + · · · + (xn − µ)2 pn .
• For any random variable X: P (X > a) = 1 − P (X ≤ a)
• If X is a Normal distribution with mean µ and standard deviation σ then Z =
standard normal distribution.
• I = P rt
• F = P (1 + rt)
r mt
• F =P 1+
m
• FV = PMT ·
[(1 + i)n − 1]
where n = mt and i =
i
• PV = PMT ·
[1 − (1 + i)−n ]
where n = mt and i =
i
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