Problem
Carlos has a spinner that is divided into 3 equal-sized sectors numbered from 1 to 3 , and a numbar cube labeled from 1 to 6 . He will spin the arrow of the spinner and roll the number cube one time. What is the probability that the arrow will land on a sector labeled 3 , and the number cube will land on a number less than 3 ? \( \frac{1}{9} \) \( \frac{2}{9} \) \( \frac{2}{3} \) \( \frac{5}{6} \)
Solution
Step 1 ：\(P(\text{sector 3}) = \frac{1}{3}\)
Step 2 ：\(P(\text{number cube} < 3) = \frac{2}{6}\)
Step 3 ：\(P(\text{sector 3} \cap \text{number cube} < 3) = \frac{1}{3} \cdot \frac{2}{6} = \frac{2}{18} = \frac{1}{9}\)
