a coin is tossed and a die is rolled. find the probability of getting a tail and a number greater than 3…

Explanation:

Step1: Calculate probability of getting a tail

A coin has 2 possible outcomes (head or tail). The probability of getting a tail, $P(T)$, is $\frac{1}{2}$ since there is 1 favorable outcome (tail) out of 2 total outcomes. So $P(T)=\frac{1}{2}$.

Step2: Calculate probability of getting a number greater than 3 on a die

A die has 6 possible outcomes ${1,2,3,4,5,6}$. The numbers greater than 3 are ${4,5,6}$, so there are 3 favorable outcomes. The probability of getting a number greater than 3, $P(N > 3)$, is $\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication - rule for independent events

Since the coin - toss and die - roll are independent events, the probability of both events occurring is the product of their individual probabilities. Let $P$ be the probability of getting a tail and a number greater than 3. Then $P = P(T)\times P(N > 3)$. Substituting the values we found: $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$