To calculate the probability of an event occurring multiple times in a row, you can multiply the probability of the event happening once by itself for the number of times it occurs.

In this case, you are trying to get a specific result (such as a "1 in 7500" event) five times in a row.

Step-by-step calculation:

1. Probability of getting 1 in 7500 once:
   The probability of getting the desired outcome (e.g., rolling a specific number) is $\frac{1}{7500}$.

2. Probability of getting it five times in a row:
   Since the events are independent (one event does not affect the next), you multiply the probability for each individual event:

   $P(\text{5 times in a row}) = \left( \frac{1}{7500} \right)^5$

3. Calculate the result:

$P(\text{5 times in a row}) = \frac{1}{7500^5} = \frac{1}{2.44140625 \times 10^{18}}$

This is an extremely small probability.

Final result:

The probability of getting "1 in 7500" five times in a row is approximately:

$P \approx 4.1 \times 10^{-19}$

So, it's about $4.1$ in one quintillion.

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Would you like further details on this? Or do you have any other questions?

Here are 5 related questions you could explore:

1. How would the probability change if we were doing this for 10 times in a row instead of 5?
2. What happens to the probability if we change the "1 in 7500" to "1 in 1000"?
3. What are the odds of getting the same result twice in a row in a series of events?
4. How does this concept apply to lottery odds?
5. How do we calculate the probability of multiple independent events?

Tip: The more independent events you try to repeat (like flipping a coin or rolling a die), the smaller the probability of all of them happening as you increase the number of trials.