Question

a number cube is rolled. what is the probability of getting a 6 a number less than 3? simplify.

Explanation:

Step1: Determine total outcomes

A number cube has 6 faces. So total outcomes \(n(S)=6\).

Step2: Find number of favorable outcomes

Numbers less than 3 are 1 and 2. Probability of getting a 6 is \(\frac{1}{6}\), probability of getting a number less than 3 is \(\frac{2}{6}\). Since these are mutually - exclusive events (can't get a 6 and a number less than 3 at the same time), use the formula \(P(A\cup B)=P(A)+P(B)\).

$$P = \frac{1}{6}+\frac{2}{6}$$

Step3: Simplify the fraction

$$P=\frac{1 + 2}{6}=\frac{3}{6}=\frac{1}{2}$$

Answer:

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