← Mathematics — Grade 8/Geometry, Measurement and Probability

Complementary Events

≈ 25 min

0/4 practice checks

Complementary Events

An event and its complement cover the whole sample space without overlap. $P(A^c)=1-P(A)$ . A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Subtract from 1.
$1-0.35=0.65$ .

Key idea

$P(A^c)=1-P(A)$ .

If $P(\text{rain})=0.35$ , find $P(\text{no rain})$ .

Which statement best captures the central mathematical idea in Complementary Events?

$P(A^c)=1-P(A)$ .

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Complementary Events, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for complementary events.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Complementary Events?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

$P(A^c)=1-P(A)$ .

Represent the given information clearly and identify the operation or relationship required for complementary events.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.

PreviousSample Spaces and Relative Frequency