Class 11 Maths Probability Axiomatic Approach

Axiomatic Approach to Probability 

It is another way of describing probability. Here Axioms or rules are used.

Let S be sample space of a random experiment containing outcomes ω1, ω2 ,...,ωn , then

  • P (ωi) ≥ 0 & P (S) = 1 è 0 ≤ P (ωi) ≤ 1
  • P (ω1) + P (ω2) + ... + P (ωn) = 1
  • For any event E, P(E) = Σ P(ωi ), ωi ∈
  • P (φ) = 0

 

 

Example: In a throw of two rigged coins, P(HH) = 1/ 4 , P(HT) = 1/ 7,  P(TH) = 2/ 7, P(TT) = 9/28  .  Find P(E) where  E = Either both head or both Tail , E = One head , one Tail, E = Both tail

Solution:

P(E) where  E = Either both head or both Tail. Since both these events are mutually exclusive events

P(HH) U P(TT) = P(HH) + P(TT)  = ¼ + 9/28  = 16/28  = 4/7

P(E) where  , E = One head.

P(HT) U P(TH) = P(HT) + P(TH)  = 1/7 + 2/7  = 3/7

P(E) where  , E = Both Tail

P(TT) =9/28

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