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Chapter 14 · Question 5

State and use the complement rule. If $P(E)=\frac35$ , find $P(\text{not }E)$ .

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Q5

State and use the complement rule. If $P(E)=\frac35$ , find $P(\text{not }E)$ .

Answer Revealed

Direct Answer:

The complement rule is

P(E)+P(\overline E)=1

. So

P(\overline E)=1-\frac35=\frac25

.

Simple Explanation

The event and its complement together cover all outcomes, so their probabilities add to 1.

Exam-Ready Structure

For any event

E

, not

E

is denoted

\overline E

. Since either

E

happens or it does not,

P(E)+P(\overline E)=1

. Thus

P(\overline E)=1-P(E)=1-\frac35=\frac25

.

Key Points

The complement rule is $P(E)+P(\overline E)=1$ .
Use the NCERT formula or theorem carefully.
Write units and final conclusion where applicable.

Related Questions

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king.

Define theoretical probability of an event.

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