To determine the probability of picking a red marble from the box, let's follow these steps:
1. Understand the Problem:
- We have a box containing three types of marbles:
- 3 black marbles
- 4 red marbles
- 5 white marbles
2. Calculate the Total Number of Marbles:
- The total number of marbles is the sum of all individual marbles.
[tex]\[
\text{Total number of marbles} = 3 \text{ (black)} + 4 \text{ (red)} + 5 \text{ (white)} = 12 \text{ marbles}
\][/tex]
3. Identify the Number of Red Marbles:
- There are 4 red marbles.
4. Determine the Probability of Picking a Red Marble:
- The probability of an event is given by the ratio of the number of favorable outcomes (in this case, the red marbles) to the total number of possible outcomes (the total number of marbles).
[tex]\[
\text{Probability of picking a red marble} = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{4}{12}
\][/tex]
5. Simplify the Fraction:
- Simplify [tex]\(\frac{4}{12}\)[/tex]:
[tex]\[
\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}
\][/tex]
6. Match the Probability with the Given Options:
- We see that [tex]\(\frac{1}{3}\)[/tex] matches option c).
Therefore, the probability that a randomly picked marble will be red is [tex]\(\frac{1}{3}\)[/tex], which corresponds to option c).
