這句中我不明may和probably放在一起 的用意及是否合文法.?

1. Yes, this sentence is grammatical correct. As matter of fact, it is pretty well written!
2. May means possible and probably means possible and likely!

1.) may probably 是否合文法?
我不知道有那一本英文文法書說這不合文法。(中文文法書我就不知道了)
也許有人會認為may 和 probably 語意重複，probably 是多餘的。這基本上是個人的偏好，無關文法。

2.)
i) ... may go to garbage bin. (有此可能性)
ii) ...may probably go to garbage bin. (此一可能性較前句大為增加)

Google Books 就有不少 may probably 的例子。
參閱 http://english.stackexchange.com/questions/227689/usage-of-the-word-probably

probably adv .most likely---probably go;
may, used to indicate possibly or probability; used to express wishes and hopes.
Items may go(=It is possible to go) for the garbage.
Subject + anomalous finite "may" are followed by a bare infinitive(without to)=Items may go.

Items may probably (adv) go.
You may find many unnecessary items when tidying up home and finally those items may probably go to garbage bin.

May系基本
Probably同may嘅意思相似,系加強語氣。

May is 可能的意思，probably 是大概，應該