If E1, E2, E3 are three mutually exclusive event and exhaustive event

1.	If E1, E2, E3 are three mutually exclusive event and exhaustive events of an experiment such that– 2P(E1) = 3P(E2) = P(E3), then find P(E1).
Answer» Since E₁, E₂, E₃ are mutually exclusive and exhaustive events, so E₁ ∩ E₂ =ϕ , E₂ ∩ E₃ = ϕ, E₁ ∩ E₃ = ϕ, E₁ ∩ E₂ ∩ E₃ = ϕ and E₁ ∪ E₂ ∪ E₃ = S ∴ p(E₁ ∪ E₂ ∪ E₃) = E₁ ∩ E₂ ∩ E₃ = ϕ p(E₁) + p(E₂) + p(E₃) ⇒ P(S) = P(E1) + \(\frac{2}{3}\)P(E₁) + 2P(F₁) ⇒ 1 = P(F₁) + \(\frac{8}{3}\)P(F₁) ⇒ \(\frac{11}{3}\)P(E₁) = 1 ⇒ P(E₁) = \(\frac{3}{11}\)

If E1, E2, E3 are three mutually exclusive event and exhaustive events of an experiment such that– 2P(E1) = 3P(E2) = P(E3), then find P(E1).

Answer»

Since E₁, E₂, E₃ are mutually exclusive and exhaustive events, so

E₁ ∩ E₂ =ϕ , E₂ ∩ E₃ = ϕ, E₁ ∩ E₃ = ϕ, E₁ ∩ E₂ ∩ E₃ = ϕ and E₁ ∪ E₂ ∪ E₃ = S

∴ p(E₁ ∪ E₂ ∪ E₃) = E₁ ∩ E₂ ∩ E₃ = ϕ p(E₁) + p(E₂) + p(E₃)

⇒ P(S) = P(E1) + \(\frac{2}{3}\)P(E₁) + 2P(F₁)

⇒ 1 = P(F₁) + \(\frac{8}{3}\)P(F₁)

⇒ \(\frac{11}{3}\)P(E₁) = 1

⇒ P(E₁) = \(\frac{3}{11}\)

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If E1, E2, E3 are three mutually exclusive event and exhaustive events of an experiment such that– 2P(E1) = 3P(E2) = P(E3), then find P(E1).

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