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Probability
Probability
7 formulas · Mathematics
Classical probability
P
(
A
)
=
∣
A
∣
∣
Ω
∣
P(A)=\dfrac{|A|}{|\Omega|}
P
(
A
)
=
∣Ω∣
∣
A
∣
Probability of the complementary event
P
(
A
′
)
=
1
−
P
(
A
)
P(A')=1-P(A)
P
(
A
′
)
=
1
−
P
(
A
)
Probability of the union of events
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
∩
B
)
P(A\cup B)=P(A)+P(B)-P(A\cap B)
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
∩
B
)
Conditional probability
P
(
A
∣
B
)
=
P
(
A
∩
B
)
P
(
B
)
P(A|B)=\dfrac{P(A\cap B)}{P(B)}
P
(
A
∣
B
)
=
P
(
B
)
P
(
A
∩
B
)
Bernoulli scheme
P
k
=
(
n
k
)
p
k
(
1
−
p
)
n
−
k
P_k=\binom{n}{k}p^k(1-p)^{n-k}
P
k
=
(
k
n
)
p
k
(
1
−
p
)
n
−
k
Expected value
E
(
X
)
=
∑
x
i
p
i
E(X)=\sum x_i p_i
E
(
X
)
=
∑
x
i
p
i
Variance of a random variable
σ
2
=
∑
(
x
i
−
E
(
X
)
)
2
p
i
\sigma^2=\sum (x_i-E(X))^2 p_i
σ
2
=
∑
(
x
i
−
E
(
X
)
)
2
p
i
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