Question

what is the probability of the complement of rolling a number less than 5 by using a six - sided die?

Explanation:

Step1: Determine the probability of rolling a number less than 5

A six - sided die has outcomes \(1,2,3,4,5,6\). The numbers less than 5 are \(1,2,3,4\). So the number of favorable outcomes \(n = 4\), and the total number of outcomes \(N=6\). The probability \(P(\text{less than }5)=\frac{4}{6}=\frac{2}{3}\).

Step2: Use the complement rule

The complement rule states that \(P(A') = 1 - P(A)\), where \(A'\) is the complement of event \(A\). Let \(A\) be the event of rolling a number less than 5. Then \(P(A')=1-\frac{2}{3}\).

$$1-\frac{2}{3}=\frac{3 - 2}{3}=\frac{1}{3}$$

Answer:

\(\frac{1}{3}\)