Question

1-71 a fair number cube with numbers 1, 2, 3, 4, 5, and 6 is rolled. a) what is the probability of getting an even number? ____ b) what is the probability of getting a factor of 6? ____

Explanation:

Part (a)

Step1: Identify total outcomes

A fair number cube has 6 faces, so total possible outcomes when rolled is \( n(S) = 6 \) (where \( S \) is the sample space).

Step2: Identify favorable outcomes (even numbers)

The even numbers on the cube are 2, 4, 6. So the number of favorable outcomes \( n(E) = 3 \) (where \( E \) is the event of getting an even number).

Step3: Calculate probability

Probability of an event \( P(E)=\frac{n(E)}{n(S)} \). Substituting the values, we get \( P(E)=\frac{3}{6}=\frac{1}{2} \).

Step1: Identify total outcomes

Total possible outcomes when rolling the cube is \( n(S) = 6 \) (same as before).

Step2: Identify factors of 6

The factors of 6 are numbers that divide 6 without leaving a remainder. The numbers on the cube that are factors of 6 are 1, 2, 3, 6. So the number of favorable outcomes \( n(F) = 4 \) (where \( F \) is the event of getting a factor of 6).

Step3: Calculate probability

Using the probability formula \( P(F)=\frac{n(F)}{n(S)} \), we substitute the values: \( P(F)=\frac{4}{6}=\frac{2}{3} \).

Answer:

\(\frac{1}{2}\)

Part (b)