Quick questions on Range of probabilities and complementary events for HSC Maths Standard 2

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the complement of an event?

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The complement of an event

E

is the event "

E

does not happen", written

\text{not } E

(you may also see

\overline{E}

E'

). If

E

is "roll a

6

" then

\text{not } E

is "roll a

1, 2, 3, 4

5

". Two facts make the complement so useful:

What is a complement pair that does not add to

1

Show answer

P(E) = 0.08

then

P(\text{not } E)

must be

0.92

, because

0.08 + 0.92 = 1

. A pair like

0.08

and

0.82

is wrong on sight, since it sums to

0.90

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