In a bag, there are 100 same-sized chips labeled 1 through 100. If one chip is selected without looking, order the probabilities of the events below by placing the event with the greatest probability on top.

To solve this problem, we need to compare the probabilities of different events when randomly selecting a chip numbered 1 through 100. The probabilities of each event depend on the number of favorable outcomes for that event.

Let's define the events more clearly and calculate their probabilities:

### Assumptions:
1. **Event A**: Probability of selecting a chip with a number divisible by 2 (even numbers).
2. **Event B**: Probability of selecting a chip with a number divisible by 3.
3. **Event C**: Probability of selecting a chip with a number divisible by 5.
4. **Event D**: Probability of selecting a chip with a number divisible by 10.

Let's find the probabilities:

1. **Event A: Divisible by 2 (Even Numbers)**  
   Numbers divisible by 2 are: 2, 4, 6, ..., 100.  
   Total numbers divisible by 2: \( \frac{100}{2} = 50 \).  
   Probability of Event A = \( \frac{50}{100} = 0.5 \).

2. **Event B: Divisible by 3**  
   Numbers divisible by 3 are: 3, 6, 9, ..., 99.  
   Total numbers divisible by 3: \( \frac{100}{3} \approx 33 \).  
   Probability of Event B = \( \frac{33}{100} = 0.33 \).

3. **Event C: Divisible by 5**  
   Numbers divisible by 5 are: 5, 10, 15, ..., 100.  
   Total numbers divisible by 5: \( \frac{100}{5} = 20 \).  
   Probability of Event C = \( \frac{20}{100} = 0.2 \).

4. **Event D: Divisible by 10**  
   Numbers divisible by 10 are: 10, 20, 30, ..., 100.  
   Total numbers divisible by 10: \( \frac{100}{10} = 10 \).  
   Probability of Event D = \( \frac{10}{100} = 0.1 \).

### Ordering the Probabilities:
Now we compare the probabilities:
- Event A: 0.5
- Event B: 0.33
- Event C: 0.2
- Event D: 0.1

The order of the events from greatest to least probability is:

1. **Event A**: Divisible by 2 (0.5)
2. **Event B**: Divisible by 3 (0.33)
3. **Event C**: Divisible by 5 (0.2)
4. **Event D**: Divisible by 10 (0.1)

Would you like more details or have any questions?

### Related Questions:
1. What is the probability of selecting a number divisible by both 2 and 3?
2. How many numbers between 1 and 100 are divisible by both 2 and 5?
3. If a number is selected randomly, what is the probability it is a prime number?
4. What is the probability of selecting a number that is divisible by either 3 or 5?
5. How would the probabilities change if the numbers were from 1 to 200 instead?

### Tip:
When dealing with probability problems, it is crucial to carefully count the favorable outcomes and ensure the total possible outcomes are correctly considered.

Explore the probabilities of selecting chips labeled 1 through 100 from a bag, comparing events such as selecting numbers divisible by 2, 3, 5, and 10. Learn how to calculate probabilities and order them effectively. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation