Question

a coin is flipped and die is rolled once. what is the probability of flipping a heads on the coin and rolling a 1 on the die? give your answer as a reduced fraction.

Explanation:

Step1: Find probability of flipping heads

A coin has 2 sides. Probability of heads $P(H)=\frac{1}{2}$.

Step2: Find probability of rolling a 1

A die has 6 sides. Probability of rolling a 1 $P(1)=\frac{1}{6}$.

Step3: Use multiplication rule for independent events

Since coin - flip and die - roll are independent, $P(H\cap1)=P(H)\times P(1)$.
$P(H\cap1)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$