What is the probability that you encounter at least one luma during the 300 encounters while using a radar?

Question

In the game Temtem there is a very small (1 out of 7500) chance that you will encounter a "luma" version of a creature. With a special radar item, you can increase these chances by encountering many of the same creature in a row. A radar lasts for 300 encounters, and changes the chances in the following way: For the first 100 encounters, the luma rate is the same as normal (1 out of 7500), for the second 100 encounters, the rate is increased by 5 times (1 out of 1500), and for the last and for the last 100 encounters the rate is increased by 10 times (1 out of 750).

Answer 1

Hi Lilly B.,

The answer depends on whether the probabilities of luma encounter at each stage are independent of each other. If you did encounter a luma in stage 1, and it ate you, for example, you would be unable to proceed to stage 2, so you would have to decrease the contribution to an encounter during stage 2 by the probability that that already took place. Similarly for stage 3.

Assuming that the luma regards you as just some incidental nibblies, that might be termed .... luma-noshity?

-- Cheers, --Mr. d.