Question

a fair die is rolled 6 times. what is the probability of having no 1 and no 4 among the rolls? round your answer to three decimal places.

Explanation:

Step1: Determine valid outcomes per roll

A fair die has 6 faces (1 - 6). We exclude 1 and 4, so valid outcomes per roll: \(6 - 2 = 4\) (faces: 2, 3, 5, 6). Probability of valid outcome per roll: \(\frac{4}{6}=\frac{2}{3}\).

Step2: Calculate probability for 6 rolls

Since each roll is independent, the probability of 6 independent events (each with probability \(\frac{2}{3}\)) is \((\frac{2}{3})^6\).
Calculate \((\frac{2}{3})^6=\frac{64}{729}\approx0.0877915\). Rounded to three decimal places: \(0.088\).

Answer:

\(0.088\)