Ehtimolning klassik, geometrik va statistik

Ehtimolliklarni ko’paytirish.

P  A / B 

Ikkita erkli hodisalarning birgalikda ro‘y berish ehtimoli, bu hodisalar ehtimollarining ko‘paytmasiga teng:
P(AB)=P(A) P(B)
Bir nechta erkli hodisalarning birgalikda ro‘y berish ehtimoli, bu hodisalar ehtimollarini ko‘paytmasiga teng:
P(A₁A₂….A_n)=P(A₁)P(A₂)….P(A_n)
Ikkita bog‘liq hodisalarning birgalikda ro‘y berish ehti-moli ulardan birining ehtimolini ikkinchisining shartli ehtimoliga ko‘paytmasiga teng.
P(AB)=P(A) P(B/A) = P(B) P(A/B)
Bir nechta bog‘liq hodisalarning birgalikda ro‘y berish ehtimoli ulardan birining ehtimolini qolganlarining shartli ehtimollariga ko‘paytirilganligiga teng, shu bilan birga, har bir keyingi hodisaning ehtimoli oldingi hamma hodisalar ro‘y berdi degan farazda hisoblanadi:
P(A₁A₂…A_n) = P(A₁) ^. P(A₂/A₁) ^. P(A₃/A₁A₂)…. P(A_n/ A₁A₂…A_n-1)
Ikkita birga ro‘y beruvchi hodisalardan kamida bittasining ro‘y berish ehtimoli shu hodisalarning ehtimollari yig‘indisidan ularning birgalikda ro‘y berish ehtimolini ayirmasiga teng:

P ( A 
B ) 
P ( A ) 
^{P ( B )  P ( AB )} .

Uchta birga ro‘y beruvchi hodisa uchun:

Agar
P ( A 
B  C ) 
P ( A ) 
P ( B ) 
P ( C )  P ( AB )  P ( AC )  P ( BC ) 
P ( ABC ).

A va B hodisalar bog‘liq bo‘lsa ,
P(A+B) = P(A) + P(B) –P(B)P(A/B)
bog‘liq bo‘lmasa P(A+B)= P(A) + P(B) – P(A) ^. P(B)

formulalaridan foydalanamiz.


Birgalikda bog‘liq bo‘lmagan A₁,A₂,…A_n hodisalaridan kamida bittasining ro‘y

berishidan iborat A hodisaning ehtimoli 1dan
 ,  , …
qarama-qarshi

1

2

^{1 2} n

n
hodisalar ehtimollari ko‘paytmasining ayir-masiga teng: ^{P(A) = 1 – P(  )P(  )…P(}  ⁾