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{smooth},\,\text{rough},\,\text{soft},\,\text{firm},\,\text{plain},\,\text{striped}\}

Event \(A\) consists of the outcomes \(\{\text{smooth},\,\text{striped}\}\)

Exact probability assigned to each outcome
Outcome	Probability
smooth	\(\frac{1}{6}\)
rough	\(\frac{1}{6}\)
soft	\(\frac{1}{6}\)
firm	\(\frac{1}{6}\)
plain	\(\frac{1}{6}\)
striped	\(\frac{1}{6}\)

(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 \(\text{smooth}\)

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

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

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

(b)1 mark

Give \(Pr(A)\) exactly

Probability of A

Format: exact fraction