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.