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 ?
\( \frac{1}{9} \)
\( \frac{2}{9} \)
\( \frac{2}{3} \)
\( \frac{5}{6} \)

Answer

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Answer

\(P(\text{sector 3} \cap \text{number cube} < 3) = \frac{1}{3} \cdot \frac{2}{6} = \frac{2}{18} = \frac{1}{9}\)

Steps

Step 1 ：\(P(\text{sector 3}) = \frac{1}{3}\)

Step 2 ：\(P(\text{number cube} < 3) = \frac{2}{6}\)

Step 3 ：\(P(\text{sector 3} \cap \text{number cube} < 3) = \frac{1}{3} \cdot \frac{2}{6} = \frac{2}{18} = \frac{1}{9}\)