1 of 8 0-day streak

Finite events, probability assignments and complements

Question 1 of 8

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A finite experiment produces exactly one outcome from the following sample space

S = \{\text{north},\,\text{east},\,\text{south},\,\text{west},\,\text{centre},\,\text{edge},\,\text{corner},\,\text{middle}\}

Event \(A\) consists of the outcomes \(\{\text{north},\,\text{east},\,\text{south},\,\text{west},\,\text{centre},\,\text{edge},\,\text{corner},\,\text{middle}\}\)

Exact probability assigned to each outcome
Outcome	Probability
north	\(\frac{1}{8}\)
east	\(\frac{1}{8}\)
south	\(\frac{1}{8}\)
west	\(\frac{1}{8}\)
centre	\(\frac{1}{8}\)
edge	\(\frac{1}{8}\)
corner	\(\frac{1}{8}\)
middle	\(\frac{1}{8}\)

(a)1 mark

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

An outcome is the whole sample space \(S\); \(S\) is the process; and \(A\) is only the one result \(\text{north}\)

An outcome is one result; the sample space \(S\) omits the possible outcome \(\text{middle}\); and \(A\) is the specified event

The experiment produces one result. An outcome is \(\text{north}\); \(S\) contains every possible outcome; and \(A\) is the specified subset of \(S\)

The experiment is the single result \(\text{north}\); \(S\) is that result; and \(A\) is the full list of outcomes

(b)1 mark

What is the probability that the outcome is in \(A\)?

Probability of A

Format: exact fraction or terminating decimal

What is \(Pr(A')\)?

Probability of A′

Format: exact fraction or terminating decimal