1 of 8 0-day streak

Single-step theoretical probability and complements

Question 1 of 8

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A collection has 7 outcome positions. One position is selected at random, and every position is equally likely

The label at each outcome position
Position	Label
\(o_{1}\)	theta
\(o_{2}\)	eta
\(o_{3}\)	alpha
\(o_{4}\)	theta
\(o_{5}\)	alpha
\(o_{6}\)	theta
\(o_{7}\)	theta

Let \(S\) be the sample space of all outcome positions. The notation \(|S|\) counts all positions, and \(|A|\) counts those in event A

Let \(A\) be the event that the selected outcome has the label "eta"

The requested event is the complement \(A^{\prime}\)

(a)1 mark

Which statement correctly describes the experiment, one outcome, the sample space \(S\) and event \(A\)?

The experiment selects one collection position. An outcome is one selected position; \(S\) contains all 7 outcome positions; and \(A\) contains position 2

An outcome is one position, \(S\) is the first 6 positions only, and \(A\) is the event

An outcome is the whole set of all possible positions, \(S\) is one selected result, and \(A\) is one outcome only

The experiment is one result, an outcome is \(S\), and \(A\) is the whole experiment

(b)1 mark

Find \(\Pr(A^{\prime})\)

Complement probability

Format: exact fraction