Probability of Drawing a Black or White Marble from a Box
In this article, we will explore the concept of probability in the context of drawing marbles from a box. We will define the problem, perform step-by-step calculations, and provide a detailed explanation to help you understand the process.
Problem Statement and Context
We have a box containing a variety of marbles, specifically 8 black marbles, 12 yellow marbles, and 5 point (let's assume these are point marbles, though their exact classification is unclear) marbles. No white marbles are mentioned in the problem. Our task is to calculate the probability of drawing a black or white marble from this box.
Step-by-Step Approach to Solving the Problem
To find the probability of a favorable outcome, we will follow a systematic approach:
Step 1: Count the Total Number of Marbles
Black marbles: 8 White marbles: 0 (since no white marbles are mentioned) Yellow marbles: 5 Point marbles: 12Total number of marbles 8 (black) 0 (white) 5 (yellow) 12 (point) 25 marbles.
Step 2: Count the Favorable Outcomes
Since the only favorable outcomes are drawing a black marble, we will only consider the black marbles:
Favorable outcomes: Black marbles: 8 White marbles: 0
Total favorable outcomes 8 (black) 0 (white) 8
Step 3: Calculate the Probability
The probability P of drawing a black or white marble is given by the formula:
P(text{black or white}) frac{text{Number of favorable outcomes}}{text{Total number of marbles}} frac{8}{25}
Alternatively, we could simplify the fraction by recognizing that:
P(text{black or white}) frac{8}{25} times 100% 32%quad text{(as a percentage)}
Alternative Interpretation and Calculation
There are also twenty-five marbles in the box, out of which twenty are either black or white. This leads to:
P(text{black or white}) frac{20}{25} frac{4}{5} 0.80 quad (as a decimal)
Common Misconceptions and Clarification
Several misconceptions can arise in probability problems. One such misconception is the idea of drawing both a black and a white marble simultaneously, which is not possible since only one marble is drawn at a time. Therefore, the probability of drawing both a black and a white marble is zero. The correct focus should be on the specific marble being drawn, in this case, a black or white marble.
Conclusion
Therefore, the probability of drawing a black or white marble is frac{8}{25} or approximately 0.32, or 32%.
Additional Insights
Understanding probability involves recognizing the distinct events and their outcomes. In the case of the black and white marbles, we have 8 favorable outcomes out of a total of 25 possible outcomes. This ratio gives us the probability of drawing a black or white marble from the box.