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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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).
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).
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) = \(\frac{3}{11}\)