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? $\frac{1}{12}$ $\frac{1}{6}$ $\frac{1}{4}$ $\frac{1}{3}$

Explanation:

Step1: Find probability of getting heads

The probability of getting heads when flipping a fair - coin is $P(H)=\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (heads).

Step2: Find probability of rolling a 5

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

Step3: Use the multiplication rule for independent events

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

Answer:

$\frac{1}{12}$