what is the probability of rolling a three on the first die and an odd number on the second die? write your…

Explanation:

Step1: Probability of rolling a 3 on first die

A die has 6 faces. The probability of rolling a 3 on the first die is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes.

Step2: Probability of rolling an odd - number on second die

The odd numbers on a die are 1, 3, 5. So there are 3 favorable outcomes out of 6 possible outcomes. The probability of rolling an odd number on the second die is $\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of both events occurring is the product of their individual probabilities. So $P=\frac{1}{6}\times\frac{1}{2}$. $P = \frac{1\times1}{6\times2}=\frac{1}{12}$

Answer:

$\frac{1}{12}$