A standard six-sided die is rolled 12 times - HSC - SSCE Mathematics Extension 1 - Question 2 - 2023 - Paper 1

To determine the probability that at least 9 of the rolls have an outcome of 2, we need to calculate the probability that the proportion p̂ of rolls that resulted in a 2 is at least 9 out of 12 rolls. This proportion can be expressed as:

$\hat{p} = \frac{9}{12} = \frac{3}{4}$

Hence, we are looking for:

$P \left( \hat{p} \geq \frac{3}{4} \right)$

Therefore, the correct answer is option A: ( P \left( \hat{p} \geq \frac{3}{4} \right) ).