Probability theory

Classical probability
$$P(A) = \frac{m}{n}$$
m - number of favorable events
n - total number of outcomes
Find   It is known that:
      =   
Calculate 'A'

Opposite probability (complement rule)
$$P(Ā) = 1-P(A)$$
P(Ā) - probability that event A will not occur
P(A) - probability that event A will occur
Find   It is known that:
      =   
Calculate 'Ā'

Probability of sum of mutually exclusive events
$$P(A+B) = P(A)+P(B)$$
Find   It is known that:
      =   
Calculate 'A'

Probability of product of mutually exclusive events
$$P(A\cdot B) = P(A)\cdot P(B)$$
Find   It is known that:
      =   
Calculate 'A'

Conditional probability
$$P(A_{NUO_B}) = \frac{P(AB)}{P(B)}$$
Find   It is known that:
      =   
Calculate 'A_NUO_B'

Bernoulli binomial probability formula
$$P_{n}\cdot (k) = C_{n}^{k}\cdot p^{k}\cdot q^{(n-k)}$$
k - number of successes
n - number of trials
p - probability of success in one trial
q = 1 - p - probability of failure in one trial
Find   It is known that:
      =   
Calculate 'P_n'

Mathematical expectation
$$EX = x_1\cdot p_1+x_2\cdot p_2+x3\cdot p3$$
EX - mathematical expectation
x1, x2, x3 ... - posible values of event
p1, p2, p3 ... - probabilities of event
Find   It is known that:
      =   
Calculate 'EX'

Dispersion (variance)
$$DX = (x_1-EX)^{2}\cdot p_1+(x_2-EX)^{2}\cdot p_2+(x3-EX)^{2}\cdot p3$$
DX - dispersion
EX - mathematical expectation
x1, x2, x3 ... - posible values of event
p1, p2, p3 ... - probabilities of event
Find   It is known that:
      =   
Calculate 'DX'

Dispersion (variance)
$$DX = (x_1^{2}\cdot p_1+x_2^{2}\cdot p_2+x3^{2}\cdot p3)-(EX)^{2}$$
DX - dispersion
EX - mathematical expectation
x1, x2, x3 ... - posible values of event
p1, p2, p3 ... - probabilities of event
Find   It is known that:
      =   
Calculate 'DX'

Standard Deviation
$$\sigma = \sqrt {DX}$$
σ - standard deviation
DX - ddispersion
Find   It is known that:
      =   
Calculate 'σ'

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