what is the probability of picking an orange marble and rolling an odd number? write your answer as a…

Explanation:

Step1: Calculate marble - picking probability

There are 12 marbles in total and 6 orange marbles. The probability of picking an orange marble $P(O)=\frac{6}{12}=\frac{1}{2}$.

Step2: Calculate dice - rolling probability

A standard die has 6 sides, and 3 of them are odd numbers (1, 3, 5). The probability of rolling an odd number $P(N)=\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate combined probability

Since the two events are independent, the probability of both events occurring is the product of their individual probabilities. $P = P(O)\times P(N)$. $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$

Answer:

$\frac{1}{4}$