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Byju's Answer

Standard XII

Mathematics

Intersection of Sets

Suppose E1,...

Question

Suppose $E_{1}, E_{2}, E_{3}$ be three mutually exclusive events such that $P (E_{i}) = p_{i}$ , for $i = 1, 2, 3$ , then
$P$ (none of $E_{1}, E_{2}, E_{3})$ equals,

0

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p_{1} + p_{2} + p_{3}

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(1 - p_{1}) (1 - p_{2}) (1 - p_{3})

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None of these

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Solution

The correct option is D None of these
Let,
$P (E_{1}) = P_{1}$
$P (E_{2}) = P_{2}$
$P (E_{3}) = P_{3}$

$P$ (none of $E_{1}, E_{2}, E_{3}) = 1 - P (E_{1} \cup E_{2} \cup E_{3})$

$= 1 - p_{1} - p_{2} - p_{3}$

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Similar questions

Suppose

E_{1}, E_{2}, E_{3}

be three mutually exclusive events such that

P (E_{i}) = p_{i}

, for

i = 1, 2, 3

p_{1} = \frac{1}{2} (1 - p), p_{2} = \frac{1}{3} (1 + 2 p)

and

p_{3} = \frac{1}{5} (2 + 3 p)

, then

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Suppose

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P (E_{i}) = p_{i}

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are the roots of

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, then value of

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E_{1}, E_{2}, E_{3}

be three mutually exclusive events such that

P (E_{i}) = p_{i}

, for

i = 1, 2, 3

then

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equals,

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. Of the three independent events

E_{1}

E_{2}

and

E_{3}

, the probability that only

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occurs is

α

, only

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occurs is

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and only

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occurs is

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E_{1}

E_{2}

E_{3}

occurs satisfy the equations

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Suppose E1,E2,E3 be three mutually exclusive events such that P(Ei)=pi, for i=1,2,3, then P (none of E1,E2,E3) equals,

The correct option is D None of theseLet,P(E1)=P1P(E2)=P2P(E3)=P3P(none of E1,E2,E3)=1−P(E1∪E2∪E3) =1−p1−p2−p3

Suppose $E_{1}, E_{2}, E_{3}$ be three mutually exclusive events such that $P (E_{i}) = p_{i}$ , for $i = 1, 2, 3$ , then
$P$ (none of $E_{1}, E_{2}, E_{3})$ equals,

The correct option is D None of these
Let,
$P (E_{1}) = P_{1}$
$P (E_{2}) = P_{2}$
$P (E_{3}) = P_{3}$

$P$ (none of $E_{1}, E_{2}, E_{3}) = 1 - P (E_{1} \cup E_{2} \cup E_{3})$

$= 1 - p_{1} - p_{2} - p_{3}$