Question

a fair die is a cube with number 1 through 6 on the sides, represented as painted spots. if a fair die is rolled, what is the probability of number 6 landing face up?

Explanation:

Identify the sample space

The sample space \(S\) of rolling a fair six-sided die consists of 6 equally likely outcomes:

$$S = \{1, 2, 3, 4, 5, 6\}$$

The total number of possible outcomes is \(n(S) = 6\).

Identify the favorable outcomes

The event \(E\) is rolling a 6. There is exactly 1 outcome that satisfies this condition:

$$E = \{6\}$$

The number of favorable outcomes is \(n(E) = 1\).

Calculate the probability

Using the theoretical probability formula:

$$P(E) = \frac{n(E)}{n(S)} = \frac{1}{6}$$

Answer:

A fair die is a cube with number 1 through 6 on the sides, represented as painted spots. If a fair die is rolled, what is the probability of number 6 landing face up? <blank>\(\frac{1}{6}\)</blank>