Probability theory

$P(A) = \frac{m}{n}$

m - number of favorable events
n - total number of outcomes

Find It is known that:

$P(Ā) = 1-P(A)$

P(Ā) - probability that event A will not occur
P(A) - probability that event A will occur

Find It is known that:

$P(A+B) = P(A)+P(B)$

Find It is known that:

$P(A\cdot B) = P(A)\cdot P(B)$

Find It is known that:

$P(A_{NUO_B}) = \frac{P(AB)}{P(B)}$

Find It is known that:

$P_{n}\cdot (k) = C_{n}^{k}\cdot p^{k}\cdot q^{(n-k)}$

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:

$EX = x_1\cdot p_1+x_2\cdot p_2+x3\cdot p3$

EX - mathematical expectation
x1, x2, x3 ... - posible values of event
p1, p2, p3 ... - probabilities of event

Find It is known that:

$DX = (x_1-EX)^{2}\cdot p_1+(x_2-EX)^{2}\cdot p_2+(x3-EX)^{2}\cdot p3$

DX - dispersion
EX - mathematical expectation
x1, x2, x3 ... - posible values of event
p1, p2, p3 ... - probabilities of event

Find It is known that:

$DX = (x_1^{2}\cdot p_1+x_2^{2}\cdot p_2+x3^{2}\cdot p3)-(EX)^{2}$

DX - dispersion
EX - mathematical expectation
x1, x2, x3 ... - posible values of event
p1, p2, p3 ... - probabilities of event

Find It is known that:

$\sigma = \sqrt {DX}$

σ - standard deviation
DX - ddispersion

Find It is known that: