The game of Monopoly has 4 railroad properties, 2 utility properties, 2 properties each of dark purple and dark blue, and 3 properties each of light blue, pink, orange, red, yellow, and green. What is the probability of NOT selecting a railroad property from the stack of property cards? Oa \frac{4}{11} Ob \frac{1}{7} Oc \
frac{6}{7} Od \frac{7}{11}
To solve this problem, we first need to find the total number of property cards in the Monopoly game and determine how many of those are railroad properties.
The Correct Answer and Explanation is:
Step 1: Count the total number of properties
From the problem:
- Railroads: 4
- Utilities: 2
- Dark Purple: 2
- Dark Blue: 2
- Light Blue: 3
- Pink: 3
- Orange: 3
- Red: 3
- Yellow: 3
- Green: 3
Now add all of them together:4 (railroads)+2 (utilities)+2+2+3+3+3+3+3+3=28 total property cards4 \text{ (railroads)} + 2 \text{ (utilities)} + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 = 28 \text{ total property cards}4 (railroads)+2 (utilities)+2+2+3+3+3+3+3+3=28 total property cards
Step 2: Find how many are not railroad properties
28 (total)−4 (railroads)=24 (non-railroads)28 \text{ (total)} – 4 \text{ (railroads)} = 24 \text{ (non-railroads)}28 (total)−4 (railroads)=24 (non-railroads)
Step 3: Find the probability of not selecting a railroad
Probability=Number of non-railroad propertiesTotal number of properties=2428=67\text{Probability} = \frac{\text{Number of non-railroad properties}}{\text{Total number of properties}} = \frac{24}{28} = \frac{6}{7}Probability=Total number of propertiesNumber of non-railroad properties=2824=76
Final Answer:
Option C: 67\frac{6}{7}76
Explanation
The game of Monopoly includes a variety of property cards which can be grouped by type. Some of the cards represent railroads while others represent utilities and color-coded real estate properties. Understanding the distribution of these cards is crucial to calculating the probability of selecting a specific type of property at random.
First, let’s determine the total number of property cards. The game features 4 railroad properties. It also includes 2 utility cards—Electric Company and Water Works. The colored property cards are grouped by color sets with varying counts. Dark Purple and Dark Blue sets each contain 2 properties. The remaining color groups—Light Blue, Pink, Orange, Red, Yellow, and Green—each contain 3 properties. Adding all of these gives us a total of 28 property cards in the game.
The question asks for the probability of not selecting a railroad property. Since 4 of the 28 cards are railroads, the remaining 24 cards are non-railroad properties. The probability of randomly picking a non-railroad card is the number of non-railroad cards divided by the total number of cards. This results in a probability of 24 out of 28, which simplifies to 6 out of 7.
This means that if you were to randomly draw one property card from the stack, there is a high likelihood—about 85.7 percent—that it will not be a railroad. This makes sense given that only 4 out of 28 cards represent railroads. Therefore, the correct answer is option C: 67\frac{6}{7}76.
