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?

Explanation:

Step1: Determine coin - flip probability

The probability of getting heads in a fair coin - flip is $\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and we want 1 of them.

Step2: Determine die - roll probability

The probability of rolling a 5 on a standard 6 - sided die is $\frac{1}{6}$ since there are 6 possible outcomes (1, 2, 3, 4, 5, 6) and we want 1 of them.

Step3: Use the multiplication rule for independent events

Since the coin - flip and the die - roll are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(\text{heads and 5})=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$