Question

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

Explanation:

Step1: Find probability of heads

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

Step2: Find probability of rolling 2

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

Step3: Multiply the probabilities

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

Answer:

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