Let Ei- i-1- 2- -n be n independent events such that PEi-1-i-1 1- i- n- the probability at least one of E1- E2- -En occurs is

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Complementary Event

Let Ei, i=1...

Question

Let $E_{i}, i = 1, 2, . . . n$ be $n$ independent events such that $P (E_{i}) = \frac{1}{i + 1} (1 \leq i \leq n)$ , the probability at least one of $E_{1}, E_{2}, . . . E_{n}$ occurs is

\frac{1}{n + 1}

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\frac{1}{n!}

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\frac{n}{n + 1}

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\frac{n + 1}{n!}

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Solution

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Similar questions

E_{i} (i = 1, 2, . . . . . . . n)

n

P (_{i}) = \frac{i}{i + 1}, 1 \leq i \leq n

n

\frac{n}{n + 1}

A_{1}, A_{2}, . . . ., A_{n}

P (A_{i}) = \frac{1}{i + 1}, i = 1, 2, . . ., n

A_{1}, A_{2}, . . . . A_{n}

E_{i}, i = 1, 2, . . . . . ., n

n

P (E_{1}) + P (E_{2}) + . . . + P (E_{n}) \leq 1

P (E_{1} \cup E_{2} \cup . . . . . \cup E_{n}) = P (E_{1}) + P (E_{2}) + . . . . . . + P (E_{n})

{lim}_{n \to \infty} (\frac{1}{n} + \frac{e^{\frac{1}{n}}}{n} + \frac{e^{\frac{2}{n}}}{n} + . . . + \frac{e^{\frac{n - 1}{n}}}{n})

n + 1

\frac{n}{n + 2}

A

E_{1}

E_{2}

P (\frac{E_{i}}{A}) = \frac{P (E_{i}) P (\frac{A}{E_{i}})}{P (E_{1}) P (\frac{A}{E_{1}}) + P (E_{2}) P (\frac{A}{E_{2}})}, i = 1, 2

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