a small wish fountain costs 1000 coins to get a wish out of, a rare is 20% a ultra rare is 10% and legendary is 8% how many times would you have to make a small wish to get a legendary

Question

a small wish fountain costs 1000 coins to get a wish out of,  a rare is 20%  a ultra rare is 10% and legendary is 8% how many times would you have to make a small wish to get a legendary

GPT-4o mini · Answer

To calculate the expected number of attempts needed to get a legendary item from the small wish fountain, we can use the probability of getting a legendary item. If the chance of getting a legendary item is 8% (or 0.08), we can find the expected number of attempts using the concept of expected value.

The expected number of tries \( E \) to get at least one legendary wish can be calculated using the formula:

\[ E = \frac{1}{p} \]

where \( p \) is the probability of getting the legendary item in a single attempt.

In this case:

\[ E = \frac{1}{0.08} = 12.5 \]

Since you can't make a fraction of a wish, you would need to make at least 13 attempts on average to have a chance of obtaining at least one legendary item. Thus, you would expect to make approximately 13 small wishes to get a legendary item.