Assertion :
Consider $E_{i}, i = 1, 2, . . . . . ., n$ as $n$ mutually exclusive events of an experiment.
$P (E_{1}) + P (E_{2}) + . . . + P (E_{n}) \leq 1$ . Reason: $P (E_{1} \cup E_{2} \cup . . . . . \cup E_{n}) = P (E_{1}) + P (E_{2}) + . . . . . . + P (E_{n})$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$E_{1}, E_{2}, . . . . ., E_{n}$ are mutually exclusive
$∴ P (E_{1} \cup$
$E_{2} \cup$
......
$\cup E_{n}) = P (E_{1}) + P (E_{2}) +$ ...... $+ P (E_{n})$
$E_{1} \cup E_{2} \cup . . . . \cup E_{n} \subseteq S$
$\Rightarrow P (E_{1} \cup E_{2} . . . . \cup E_{n}) \leq 1$
$\Rightarrow P (E_{1}) + P (E_{2}) + P (E_{3}) + . . . . . + P (E_{n}) \leq 1$

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Similar questions

Assertion : In rolling a die, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason : In a sample space two events are mutually exclusive if they do not occur at the same time.

Assertion: In rolling a dice, event A = {1, 3, 5} and event B = {2, 4} are mutually exclusive events.
Reason: In a sample space, two events are mutually exclusive if they do not occur at the same time.

ASSERTION: n-Pentane and n-Hexane belong to a homologous series.

REASON: n-Pentane and n-Hexane belong to the same class of hydrocarbons and they differ by a - $C H_{2}$ - group.

Q. Assertion: The compressibility factor for

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and

H e

(1 + \frac{P b}{R T})

Reason: The compressibility factor for

H_{2}

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H e

can be derived from Van der Waal's equation.

Q. Assertion : Two electrons of helium atom are placed in only one shell but three electrons of lithium need two shells.
Reason: A shell can have maximum

{2n}^{2}

electrons.

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Assertion :Consider Ei,i=1,2,......,n as n mutually exclusive events of an experiment.P(E1)+P(E2)+...+P(En)≤1. Reason: P(E1∪E2∪.....∪En)=P(E1)+P(E2)+......+P(En).

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionE1,E2,.....,En are mutually exclusive∴P(E1∪E2∪......∪En)=P(E1)+P(E2)+......+P(En)E1∪E2∪....∪En⊆S⇒P(E1∪E2....∪En)≤1⇒P(E1)+P(E2)+P(E3)+.....+P(En)≤1

Assertion :
Consider $E_{i}, i = 1, 2, . . . . . ., n$ as $n$ mutually exclusive events of an experiment.
$P (E_{1}) + P (E_{2}) + . . . + P (E_{n}) \leq 1$ . Reason: $P (E_{1} \cup E_{2} \cup . . . . . \cup E_{n}) = P (E_{1}) + P (E_{2}) + . . . . . . + P (E_{n})$ .