what is the probability of flipping tails and rolling an even number? write your answer as a fraction or a…

Explanation:

Step1: Probability of flipping tails

A coin has 2 sides. The probability of flipping tails, $P(T)$, is $\frac{1}{2}$ since there is 1 tail - side out of 2 possible outcomes.

Step2: Probability of rolling an even number

A standard die has 6 sides, and the even - numbered sides are 2, 4, 6. So there are 3 even - numbered sides out of 6 possible outcomes. The probability of rolling an even number, $P(E)$, is $\frac{3}{6}=\frac{1}{2}$.

Step3: Probability of both events

Since the coin - flip and die - roll are independent events, the probability of both events occurring is the product of their individual probabilities. Using the formula $P(A\cap B)=P(A)\times P(B)$, we have $P(T\cap E)=P(T)\times P(E)$. Substituting the values we found, $P(T\cap E)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$