if you flip a coin and roll a 6 - sided die, what is the probability that you will flip a heads and roll an…

Explanation:

Step1: Calculate coin - flip probability

The probability of flipping a head on a fair coin is $P(H)=\frac{1}{2}$ since there are 2 possible outcomes (head or tail).

Step2: Calculate die - roll probability

The probability of rolling an even number on a 6 - sided die. The even numbers on a 6 - sided die are 2, 4, 6. So there are 3 favorable outcomes out of 6. Thus $P(E)=\frac{3}{6}=\frac{1}{2}$.

Step3: Use 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 $P = P(H)\times P(E)$. Substitute $P(H)=\frac{1}{2}$ and $P(E)=\frac{1}{2}$ into the formula: $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$