Question

a coin is flipped, then a number cube is rolled. the tree diagram shows the possible outcomes. what is p(heads, then 2)? options: \\(\frac{1}{12}\\), \\(\frac{1}{6}\\), \\(\frac{7}{12}\\), \\(\frac{5}{6}\\)

Explanation:

Step1: Probability of Heads

A coin has 2 outcomes (heads, tails), so \( P(\text{heads}) = \frac{1}{2} \).

Step2: Probability of 2 on Cube

A number cube (die) has 6 outcomes, so \( P(2) = \frac{1}{6} \).

Step3: Multiply Probabilities (Independent Events)

For independent events, \( P(A \text{ and } B) = P(A) \times P(B) \). Thus, \( P(\text{heads, then } 2) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \).

Answer:

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