Question

britney will flip a coin and then roll a standard 6 - sided die. this tree diagram represents the possible outcomes. what is the probability that the coin lands on heads and then britney rolls a 5? options: \\(\frac{1}{12}\\), \\(\frac{1}{6}\\), \\(\frac{1}{4}\\), \\(\frac{1}{3}\\)

Explanation:

Step1: Probability of coin heads

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

Step2: Probability of die roll 5

A die has 6 outcomes, so \( P(\text{roll 5}) = \frac{1}{6} \).

Step3: Multiply probabilities (independent events)

\( P(\text{heads and 5}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \).

Answer:

\(\frac{1}{12}\) (corresponding to the option with \(\frac{1}{12}\))