Question

A box contains 20 marbles, all of which are solid colored; 5 of the marbles are green and 10 of the marbles are red.
Column A: The probability that a marble selected at random from the box will be green
Column B: The probability that a marble selected at random from the box will be neither red nor green

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When dealing with probability questions involving categories, always make sure you account for all items. Calculating the number of items in the "other" or "neither" category is often the first and most crucial step.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem requires calculating and comparing two probabilities based on the composition of marbles in a box.
Step 2: Key Formula or Approach:
The probability of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
Step 3: Detailed Explanation:
First, let's determine the number of marbles of each type.
Total marbles = 20.
Green marbles = 5.
Red marbles = 10.
Number of marbles that are neither red nor green = Total marbles - (Green marbles + Red marbles)
\[ = 20 - (5 + 10) = 20 - 15 = 5 \]
So, there are 5 marbles that are neither red nor green.
Calculate the quantity in Column A:
The probability of selecting a green marble is:
\[ P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{5}{20} = \frac{1}{4} \]
Calculate the quantity in Column B:
The probability of selecting a marble that is neither red nor green is:
\[ P(\text{neither red nor green}) = \frac{\text{Number of marbles that are not red or green}}{\text{Total number of marbles}} = \frac{5}{20} = \frac{1}{4} \]
Step 4: Final Answer:
The quantity in Column A is \(\frac{1}{4}\) and the quantity in Column B is \(\frac{1}{4}\). The two quantities are equal.