need help w probability

[tardy egret]

i need help

[distant hull]

I suppose that probability of two different fruits isnt just 8x/(x+8)(x+7). Since its 2 different fruits it can be Apple -> Banana or Banana -> Apple. Which basically would be just double of previous probability 16x/(x+8)(x+7) because they are the same. And Im still quite confused why its 16/35 and not 48/95.

[tardy egret]

Drew a tree diagram thinking it would help

Excuse my handwriting

[distant hull]

I see the idea of what you're trying to do. But still why not to try to solve it as an equation? Well we already have probability of selecting two different fruits which is 48/95. And as I was stating earlier we have somewhat formula to this. I'd like to elaborate why its 16x/(x+8)(x+7). So Apple -> Orange is 8x/(x+8)(x+7) obviously, as you already wrote that down in the first image. But also Orange -> Apple is the same. Then we sum these 2 probabilites to get one. Why? Well because its stated 'in ANY ORDER' and 'of selecting two DIFFERENT fruits' so I supposed that it would be logical to do that. And just by looking at 16x/(x+8)(x+7) we can already see that numerator is greater than demunator thus the chance will be higher than if it would be 8x/(x+8)(x+7) which wouldnt probably be 'in any order'.

[tardy egret]

girl/boy, dum it down, i beg you

[distant hull]

Lol lemme simplify it in that case. So 'apple -> banana' and 'banana -> apple' (and I just realized that last message i wrote those as oranges and not bananas) are the same. 8x/(8+x)(7+x)
Why we sum these 2? Because it says 'in any order' so it doesnt matter if its 'apple -> banana' or 'banana -> apple'.
Thats why in the end we get 16x/(x+8)(x+7)

And then I suggest you to solve this via making equation. We got the 16x/(x+8)(x+7) and we got the 48/95. And yea they are equal.

[tardy egret]

thanks brother/sister

have agood one