Suppose a bag contains $3$ orange marbles and $5$ blue marbles. If you randomly pick one marble from the bag and then flip a fair coin, what is the probability of picking an orange marble and flipping tails?

• A. $\frac{1}{2}$
• B. $\frac{3}{16}$
• C. $\frac{3}{8}$
• D. $\frac{5}{16}$

Answer: (B)

Verified step by step guidance

1. Identify the total number of marbles in the bag by adding the number of orange marbles and blue marbles: total marbles = 3 + 5.
2. Calculate the probability of picking an orange marble by dividing the number of orange marbles by the total number of marbles: \(\frac{3}{8}\).
3. Recognize that the coin is fair, so the probability of flipping tails is \(\frac{1}{2}\).
4. Since picking a marble and flipping a coin are independent events, multiply their probabilities to find the combined probability: \(\frac{3}{8} \times \frac{1}{2}\).
5. Express the final probability as a simplified fraction representing the chance of both picking an orange marble and flipping tails.