Multiplication Law of Probability

The probability of simultaneous occurence of two events for A and B

P(A⋂B)= P(A)xP(B|A) P(AB)=P(A)xP(B|A)

The above equation can be interchanged

P(AB)=P(A)xP(B|A) When Interchanged with each other: P(BA)=P(B)xP(A|B) P(AB)=P(B)xP(A|B) [Since, B⋂A=A⋂B]

If A and B are independednt events, then

P(B|A)=P(B) P(AB)=P(A)xP(B)

General Soultion: If (A₁, A₂, A₃... A_n) are n independent events, then P(A₁)xP(A₂)xP(A₃)...P(A_n)

If P is the chance that an will happen in one trial then that chance that it will happen in a succession of trials.

P.P.P....P(r times)=P^r

If P₁, P₂, ... P_n are the probabilities that contain events happen then the probabilities are:

(1-P₁)(1-P₂) ... (1-P_n)

Hence, the chance in which atleast one of these event much happen is:

1-(1-P₁)(1-P₂)(1-P₃)... (1-P_n)