If the numbers on the chips range from 40 to 100, rather than from 1 to 100, the total number of chips becomes smaller. Let's recalculate the probabilities for the events based on this new range of numbers.

Assumptions:

The chips are numbered from 40 to 100. This means there are a total of:

$\text{Total numbers} = 100 - 40 + 1 = 61$

We will now calculate the probabilities for the four events.

Events:

1. Event A: Divisible by 2 (Even Numbers)
2. Event B: Divisible by 3
3. Event C: Divisible by 5
4. Event D: Divisible by 10

Calculations:

1. Event A: Divisible by 2 (Even Numbers)
   Even numbers between 40 and 100 are: 40, 42, 44, ..., 100.
   Total even numbers:
   $\text{Count} = \frac{100 - 40}{2} + 1 = \frac{60}{2} + 1 = 30 + 1 = 31$
   Probability of Event A = $\frac{31}{61} \approx 0.508$.

2. Event B: Divisible by 3
   Numbers divisible by 3 between 40 and 100 are: 42, 45, 48, ..., 99.
   Total numbers divisible by 3:
   $\text{Count} = \left\lfloor \frac{100}{3} \right\rfloor - \left\lfloor \frac{39}{3} \right\rfloor = 33 - 13 = 20$
   Probability of Event B = $\frac{20}{61} \approx 0.328$.

3. Event C: Divisible by 5
   Numbers divisible by 5 between 40 and 100 are: 40, 45, 50, ..., 100.
   Total numbers divisible by 5:
   $\text{Count} = \left\lfloor \frac{100}{5} \right\rfloor - \left\lfloor \frac{39}{5} \right\rfloor = 20 - 7 = 13$
   Probability of Event C = $\frac{13}{61} \approx 0.213$.

4. Event D: Divisible by 10
   Numbers divisible by 10 between 40 and 100 are: 40, 50, 60, ..., 100.
   Total numbers divisible by 10:
   $\text{Count} = \left\lfloor \frac{100}{10} \right\rfloor - \left\lfloor \frac{39}{10} \right\rfloor = 10 - 3 = 7$
   Probability of Event D = $\frac{7}{61} \approx 0.115$.

Ordering the Probabilities:

Now we compare the probabilities:

• Event A: 0.508
• Event B: 0.328
• Event C: 0.213
• Event D: 0.115

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

1. Event A: Divisible by 2 (0.508)
2. Event B: Divisible by 3 (0.328)
3. Event C: Divisible by 5 (0.213)
4. Event D: Divisible by 10 (0.115)

Would you like more details or have any questions?

Related Questions:

1. How would the probabilities change if the numbers were between 50 and 150 instead?
2. What is the probability of selecting a number divisible by both 2 and 5 in this range?
3. How many numbers between 40 and 100 are divisible by both 3 and 5?
4. What is the probability of selecting a number that is not divisible by 2, 3, 5, or 10?
5. If a number is selected randomly, what is the probability it is a prime number?

Tip:

For problems involving ranges and divisibility, breaking down the range step-by-step and using integer division helps in accurately counting the favorable outcomes.