How many times do i need to choose a fruit before i get an apple (on average)?

[Bugsyau]

I am hatching game eggs that contain special pets. Every egg i hatch has a pet.
There are 6 possible pets.

The chances of getting a specific pet is as follows:
* bottle pet - 35% chance to get when hatching an egg
* box pet - 27% chance to get when hatching an egg
* car pet - 23% chance to get when hatching an egg
* scooter pet - 14% chance to get when hatching an egg
* house pet - 0.05% chance to get when hatching an egg
* tree pet - 0.0017% chance to get when hatching an egg

Can I determine roughly how many eggs i would have to hatch to get a tree pet? ie,is it a 1 in 17k chance of getting a tree pet from an egg? -so in theory if i hatch 17k eggs i am highly likely to get a tree pet from one? or is the math not obtainable since every egg hatch has the same chance to get a tree pet and getting 100 bottle pets doesn't change the possibility of getting a tree pet from the next hatch?

 

[stapel]

I am hatching game eggs that contain special pets. Every egg i hatch has a pet.
There are 6 possible pets.

The chances of getting a specific pet is as follows:
* bottle pet - 35% chance to get when hatching an egg
* box pet - 27% chance to get when hatching an egg
* car pet - 23% chance to get when hatching an egg
* scooter pet - 14% chance to get when hatching an egg
* house pet - 0.05% chance to get when hatching an egg
* tree pet - 0.0017% chance to get when hatching an egg

These probabilities do not sum to [imath]100[/imath]:

[imath]\qquad 35+27+23+14+0.05 = 99.05[/imath]

Another [imath]0.95%[/imath] that needs to be accounted for.

 

[Dr.Peterson]

Can I determine roughly how many eggs i would have to hatch to get a tree pet? ie,is it a 1 in 17k chance of getting a tree pet from an egg? -so in theory if i hatch 17k eggs i am highly likely to get a tree pet from one? or is the math not obtainable since every egg hatch has the same chance to get a tree pet and getting 100 bottle pets doesn't change the possibility of getting a tree pet from the next hatch?

We can presumably ignore all the other numbers and just use the fact that the probability of getting a tree is 0.0017.

But that is not 1/17000; it's 17/10000, which is about 1/588. So you would expect that about 1 in 588 tries would give you a tree.

That, however, is not "how many eggs I would have to hatch to get a tree".

As you indicate, you can't calculate when you could be sure of a tree; but you could calculate how many you need in order to have, say, a 95% chance of getting at least one tree (or however you choose to define "highly likely"; or the expected number of tries before you get a tree (that is, how long it would take on average).

Are you familiar with any of these ideas? Do you know how to calculate the probably of at least one success in N tries?