If events nbsp- nbsp-E1- nbsp-E2- nbsp-En nbsp- nbsp-represent a partition of sample space S-Then which of the following is-are correct-

A set of events nbsp; E1, nbsp;E2, nbsp;..., nbsp;En is said to represent a partition of the sample space S if nbsp; Ei∩Ej nbsp;= nbsp;ϕ, nbsp;i ...

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Byju's Answer

Standard XII

Mathematics

Partition of Sample Space

If events n...

Question

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 options are
A $E_{1} \cap E_{2} = ϕ$
C $E_{1} \cup E_{2} \cup . . . \cup E_{n} = S$
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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Similar questions

If $E_{1}, E_{2}, E_{3} \dots E_{n}$ are n events of a sample space S and if $E_{1} \cup E_{2} \cup E_{3} \cup \dots E_{n} = S$ , then $E_{1}, E_{2} \dots E_{n}$ are called mutually exclusive and exhaustive events.

Q. If events

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

represent a partition of sample space S.
Then which of the following is/are correct?

Q. Events

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

are ______ events if their union is the sample space

S

Q. The events

E_{1}, E_{2}, . . . . . . . .

represents the partition of the sample space

S

, if they are:

Q. Match the following

If $E_{1}$ and $E_{2}$ are the mutually exclusive events	A	i	$E_{1} \cap E_{2} = E_{1}$
If $E_{1}$ and $E_{2}$ are the mutually exclusive and exhaustive events	B	ii	$(E_{1} - E_{2}) \cup (E_{1} \cap E_{2}) = E_{1}$
If $E_{1}$ and $E_{2}$ have common outcomes, then	C	iii	$E_{1} \cap E_{2} = ϕ, E_{1} \cup E_{2} = S$
If $E_{1}$ and $E_{2}$ are two events such that $E_{1} \subset E_{2}$	D	iv	$E_{1} \cap E_{2} = ϕ$

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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 options are A E1∩E2 = ϕ C E1∪E2 ∪...∪ En = S 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?