Question

A marble is to be drawn at random from a bag that contains 2 yellow marbles, 4 blue marbles, 6 green marbles, and no other marbles.
 

Column A	Column B
The probability that the marble drawn will be green	The probability that the marble drawn will be yellow or blue

 

Hint:

In probability questions, sometimes you don't need to calculate the final value. You can simply compare the number of favorable outcomes. In this case, there are 6 green marbles (Column A) and 6 yellow-or-blue marbles (Column B). Since the total is the same for both, the probabilities must be equal.

Answer 1

Step 1: Understanding the Concept:
This problem requires the calculation and comparison of probabilities from a set of objects. The key is to first determine the total number of outcomes.
Step 2: Key Formula or Approach:
The probability of an event is calculated as:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] The probability of either of two mutually exclusive events (like drawing a yellow or a blue marble) is the sum of their individual probabilities.
Step 3: Detailed Explanation:
First, calculate the total number of marbles in the bag:
Total marbles = 2 (yellow) + 4 (blue) + 6 (green) = 12 marbles.
For Column A:
The probability of drawing a green marble.
Number of favorable outcomes (green marbles) = 6.
\[ P(\text{green}) = \frac{6}{12} = \frac{1}{2} \] For Column B:
The probability of drawing a yellow or blue marble.
Number of favorable outcomes (yellow or blue) = 2 + 4 = 6.
\[ P(\text{yellow or blue}) = \frac{6}{12} = \frac{1}{2} \] Alternatively, \(P(\text{yellow or blue}) = P(\text{yellow}) + P(\text{blue}) = \frac{2}{12} + \frac{4}{12} = \frac{6}{12} = \frac{1}{2}\).
Step 4: Final Answer:
Both Column A and Column B have a value of \(\frac{1}{2}\). Therefore, the two quantities are equal.