Maths question for probability

[SoulGuardian.6203]

If you are a mathematics genious and expert, 

I have a question for you about probability.

 

Say you want to buy a 5 randomly picked mounts out of a possible 15.

 

2 Raptors

2 Bunnies 

2 skimmers

2 Jackals

4 beetles

3 gryphons

 

Let's say for instance, what are the probabilities of getting a beetle skin?

You have 5 chances.

 

I know it's a hard question, but I am really bad at maths generally, and hope someone can help me make the decision to go for 5 random ones or just straight get the select licence one.

 

Thanks in advance. 

[Jijimuge.4675]

It's fairly straightforward, but just to confirm what you mean, you're asking what are the odds of getting *at least* one beetle skin?  I'm assuming that you're asking re any one of the 4 beetle skins in your list rather than 1 specific beetle skin, btw.

If so, the probability can best be looked at as 100% minus the chance of getting no beetle skin on any of your random rolls.

For the first roll, your chance of getting no beetle skin is 11/15 = 73.3% (as there are 15 potential mounts, and 11 of them are non-beetles)

For the 2nd roll, you've used up one of the non-beetle skins, but there are also 14 skins in total left to choose from, so the odds of getting no beetle skin on your second roll are 10/14 = 71.4%

One can go on with rolls 3, 4 and 5 to get odds of 9/13, 8/12 and 7/11 respectively

So the odds of getting *no* beetle skins at all with 5 rolls is 11/15 x 10/14 x 9/13 x 8/12 x 7/11 = appx 15.4%

Thus, the odds of getting *at least* one beetle skin are 100% minus 15.4% = approx 84.6%, which is the chance you were looking for. 

Of course, there's also a chance that you get 2 or beetle skins through this process, but that's another calculation.

[SoulGuardian.6203]

1 hour ago, Jijimuge.4675 said:

It's fairly straightforward, but just to confirm what you mean, you're asking what are the odds of getting *at least* one beetle skin?  I'm assuming that you're asking re any one of the 4 beetle skins in your list rather than 1 specific beetle skin, btw.

If so, the probability can best be looked at as 100% minus the chance of getting no beetle skin on any of your random rolls.

For the first roll, your chance of getting no beetle skin is 11/15 = 73.3% (as there are 15 potential mounts, and 11 of them are non-beetles)

For the 2nd roll, you've used up one of the non-beetle skins, but there are also 14 skins in total left to choose from, so the odds of getting no beetle skin on your second roll are 10/14 = 71.4%

One can go on with rolls 3, 4 and 5 to get odds of 9/13, 8/12 and 7/11 respectively

So the odds of getting *no* beetle skins at all with 5 rolls is 11/15 x 10/14 x 9/13 x 8/12 x 7/11 = appx 15.4%

Thus, the odds of getting *at least* one beetle skin are 100% minus 15.4% = approx 84.6%, which is the chance you were looking for. 

Of course, there's also a chance that you get 2 or beetle skins through this process, but that's another calculation.

 

Thank you so much.

That's pretty impressive.