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Partition of Sample Space

If events E 1...

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

Q. The events

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

represents the partition of the sample space

S

, if they are:

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. Events

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

are ______ events if their union is the sample space

S

E_{1} a n d E_{2}

are events in a probability space satisfying the following constraints

P (E_{1}) = P (E_{2}); P (E_{1} \cup E_{2}) = 1; E_{1} a n d E_{2}

are independent then

P (E_{1}) =

Q. Let

S

be the sample space of all

3 \times 3

matrices with entries from the set {0,1}. Let the events

E_{1}

and

E_{2}

be given by

E_{1} = {A \in S : d e t A = 0}

and

E_{2} =

\in S :

sum of entries of

A

7

}
If the matrix is chosen at random from

S,

then the conditional probability

P (E_{1} | E_{2})

equals

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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?