Question

while playing a board game, you roll two different colored standard dice. what is the probability of rolling a 5 on the black die and a number less than 4 on the red die? (1 point) 1/12 1/10 1/2 2/3

Explanation:

Step1: Calculate probability for black die

The black die has 6 faces. Probability of rolling a 5 is \( P(\text{black})=\frac{1}{6}\)

Step2: Calculate probability for red die

Numbers less than 4 on a die: 1, 2, 3. So \( P(\text{red})=\frac{3}{6}=\frac{1}{2}\)

Step3: Use multiplication rule for independent events

Since the rolls are independent, \( P = P(\text{black})\times P(\text{red})=\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}\)

Answer:

\(\frac{1}{12}\) (First option)