what are the chances

3.6% chance of finding one into a treasure chest, which means:

* 96.4% chance of you finding anything else but the auto-petter
* 96.4% chance of your friend finding anything else but the auto-petter
* 0.1296% chance of you AND your friend both finding the auto-petter
* 7.0704% chance of you OR your friend OR both finding an auto-petter
* 6.9408% chance of any one of you but not both finding an auto-petter
* 92.9296% chance of neither you nor your friend finding an auto-petter
* 3.4704% chance of you finding the auto-petter but not your friend
* 3.4704% chance of your friend finding the auto-petter but not you

Y is you. F is your friend.

P(Y’) = 1 – P(Y)

P(Y’) = 1 – 0.036

P(Y’) = 0.964

—

P(F’) = 1 – P(F)

P(F’) = 1 – 0.036

P(F’) = 0.964

—

P(Y∩F) = P(Y) × P(F)

P(Y∩F) = 0.036 × 0.036

P(Y∩F) = 0.001296

—

P(Y∪F) = P(Y) + P(F) – P(Y∩F)

P(Y∪F) = 0.036 + 0.036 – 0.001296

P(Y∪F) = 0.070704

—

P(YΔF) = P(Y) + P(F) – 2P(Y∩F)

P(YΔF) = 0.036 + 0.036 – 2×0.001296

P(YΔF) = 0.069408

—

P((Y∪F)’) = 1 – P(Y∪F)

P((Y∪F)’) = 1 – 0.070704

P((Y∪F)’) = 0.929296

—

P(Y occur but NOT F) = P(Y) × (1- P(F))

P(Y occur but NOT F) = 0.036 × (1 – 0.036)

P(Y occur but NOT F) = 0.034704

—

P(F occur but NOT Y) = (1 – P(Y)) × P(F)

P(F occur but NOT Y) = (1 – 0.036) × 0.036

P(F occur but NOT Y) = 0.034704