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

Explanation:

Step1: Calculate probability of picking orange marble

There are 4 orange marbles and 10 marbles in total. So the probability $P(O)$ of picking an orange marble is $\frac{4}{10}=\frac{2}{5}$.

Step2: Calculate probability of rolling an even - number

A standard die has 6 sides, and 3 of them are even numbers (2, 4, 6). So the probability $P(E)$ of rolling an even number is $\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since picking a marble and rolling a die are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P(O)\times P(E)$. $P=\frac{2}{5}\times\frac{1}{2}$ $P=\frac{2\times1}{5\times2}=\frac{1}{5}$

Answer:

$\frac{1}{5}$