If events $E_{1}, E_{2}, . . ., E_{n}$ represent a partition of sample space S.
Then which of the following is/are correct?

E_{1} \cap E_{2} = ϕ

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E_{1} \cap E_{2} \neq ϕ

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E_{1} \cup E_{2} \cup . . . \cup E_{n} = S

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P (E_{i}) > 0 for all i = 1, 2, \dots, n

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Solution

The correct option is D $P (E_{i}) > 0 for all i = 1, 2, \dots, n$
A set of events
$E_{1}, E_{2}, . . ., E_{n}$ is said to represent a partition of the sample space S if
$E_{i} \cap E_{j} = ϕ, i \neq j, i, j = 1, 2, \dots, n$
$E_{1} \cup E_{2} \cup . . . \cup E_{n} = S$
and
$P (E_{i}) > 0 for all i = 1, 2, . . ., n$

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If events E1, E2,..., En represent a partition of sample space S. Then which of the following is/are correct?

The correct option is D P(Ei) > 0 for all i = 1, 2, ⋯, nA set of events E1, E2, ..., En is said to represent a partition of the sample space S if Ei∩Ej = ϕ, i≠j, i, j = 1, 2,…, n E1∪E2∪...∪En = S and P(Ei) > 0 for all i = 1, 2, . . ., n

If events $E_{1}, E_{2}, . . ., E_{n}$ represent a partition of sample space S.
Then which of the following is/are correct?