1 of 8 0-day streak

Design and interpret a probability simulation

Question 1 of 8

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A target experiment selects one item from a finite population. The category counts are low: 4, middle: 2, high: 1, peak: 1, with total 8

The selected item is returned before the next trial. Let \(E\) be the event that the outcome is high or peak

The target probability is \(\Pr(E)\) = \(\frac{1}{4}\)

The simulation used the following procedure

Use a container holding 32 equally likely numbered tokens

Map outcomes 1 to 16 to low, outcomes 17 to 24 to middle, outcomes 25 to 28 to high and outcomes 29 to 32 to peak

Reset the device before the next trial

Treat one complete selection as one trial

Run 1 recorded low: 9, middle: 2, high: 3, peak: 2, giving 16 trials in total

(a)2 marks

Record the two counts needed to estimate the probability from the run or runs

Successful trials in Run 1 Total trials in Run 1

(b)1 mark

Calculate the Run 1 estimate as a fraction or terminating decimal

Run 1 relative frequency

Format: exact fraction or terminating decimal

Choose the statement that interprets this simulated result correctly

The finite run gives no sample proportion that can be interpreted

The sample proportion is below the target probability \(\Pr(E)\)

The sample proportion matches the target probability exactly

The sample proportion is above the target probability \(\Pr(E)\)