The Probability that at least one of the events `E_(1)` and `E_(2)` will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find `P(barE_(1))+P(barE_(2))`

The Probability that at least one of the events `E_(1)` and `E_(2)` wi

1.	The Probability that at least one of the events `E_(1)` and `E_(2)` will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find `P(barE_(1))+P(barE_(2))`
Answer» Given, `P(E_(1) uu E_(2)) = 0.6 and P(E_(1) nn E_(2)) = 0.2.` `therefore P(E_(1) uu E_(2)) = P(E_(1)) + P(E_(2)) - P(E_(1) nn E_(2))` `rArr P(E_(1)) + P(E_(2)) = P(E_(1) uu E_(2)) + P(E_(1) nn E_(2)) = (0.6 + 0.2) = 0.8` `rArr P(E_(1)) + P(E_(2)) = 0.8` `rArr {1 - P(bar(E_(1)))} + {1 + P(bar(E_(2)))} = 0.8` `rArr P(bar(E_(1))) + P(bar(E_(2))) = (2 - 0.8) = 1.2.` Hence, `P(bar(E_(1))) + P(bar(E_(2))) = 1.2.`

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The Probability that at least one of the events `E_(1)` and `E_(2)` will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find `P(barE_(1))+P(barE_(2))`

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