Jerry is rolling a six-sided die. How much more likely is it (expressed as a percentage) that he rolls a number greater than 3 than that he rolls two even numbers in a row?

We are given two events: 
1. Rolling a number greater than 3 on a six-sided die.
2. Rolling two even numbers in a row on a six-sided die.

We need to determine how much more likely the first event is compared to the second, expressed as a percentage.

### Step 1: Probability of rolling a number greater than 3
On a six-sided die, the numbers greater than 3 are: 4, 5, and 6. So, there are 3 favorable outcomes.

Thus, the probability of rolling a number greater than 3 is:
\[
P(\text{greater than 3}) = \frac{3}{6} = \frac{1}{2} = 0.5
\]

### Step 2: Probability of rolling two even numbers in a row
The even numbers on a six-sided die are: 2, 4, and 6. So, there are 3 favorable outcomes for each roll.

The probability of rolling an even number on one roll is:
\[
P(\text{even number}) = \frac{3}{6} = \frac{1}{2} = 0.5
\]

The probability of rolling two even numbers in a row (independent events) is:
\[
P(\text{two even numbers in a row}) = P(\text{even}) \times P(\text{even}) = 0.5 \times 0.5 = 0.25
\]

### Step 3: Comparison and percentage difference
Now, we compare the probabilities:
- Probability of rolling a number greater than 3: \( 0.5 \)
- Probability of rolling two even numbers in a row: \( 0.25 \)

To find how much more likely the first event is than the second, we calculate the percentage increase:
\[
\text{Percentage increase} = \left( \frac{0.5 - 0.25}{0.25} \right) \times 100 = \left( \frac{0.25}{0.25} \right) \times 100 = 100\%
\]

Thus, rolling a number greater than 3 is 100% more likely than rolling two even numbers in a row.

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Would you like more details or have any questions? Here are some related questions to further explore this problem:

1. What is the probability of rolling an odd number on a six-sided die?
2. How would the probability change if Jerry rolls a die with more sides?
3. What is the probability of rolling three even numbers in a row?
4. How would we calculate the probability of rolling two numbers greater than 3 in a row?
5. What is the probability of rolling a number less than or equal to 3?

**Tip:** When dealing with independent events, multiply the probabilities of individual events to find the combined probability.

Explore how to calculate the probability of rolling a number greater than 3 compared to rolling two even numbers in a row on a six-sided die. This problem covers key probability concepts and includes a detailed step-by-step solution suitable for students in Grades 8-10.

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