Question

in this game there are item boxes and for the best item its a 0.02% chance of getting it how many item boxes do i need to get it

Answer 1

To calculate the expected number of item boxes you would need to open to get a rare item with a probability of 0.02%, you can use the concept of expected value in probability.

If the chance of getting the item in one box is 0.02% (or 0.0002), the probability of **not** getting the item is:

\[
1 - 0.0002 = 0.9998
\]

The expected number of boxes needed to get at least one item can be calculated using the formula for the expected value of a geometric distribution, which is:

\[
E(X) = \frac{1}{p}
\]

where \( p \) is the probability of success (in this case, getting the item from a box).

Thus,

\[
E(X) = \frac{1}{0.0002} = 5000
\]

So, on average, you would need to open **5000 item boxes** to expect to get the best item with a 0.02% chance.