Group by change the sql plan by adding "filter"

Question

The table is created by:
SQL> create table t1 as select  1 a,rownum b, rownum c from dual connect by rownum<10000;
Table created.
SQL> create index t1_idx on t1 (a,b);
Index created.
SQL> exec dbms_stats.gather_table_stats(null,'T1',cascade=>true,estimate_percent=>1,no_invalidate=>true,degree=>4,block_sample => true,granularity => 'ALL');
PL/SQL procedure successfully completed.After added group by, the access and filter appear in the plan, and they are exactly the same
SQL> set autotrace trace explain
SQL> select b,count(*) from t1 where a=1 and b between 10 and 200 group by b;
Execution Plan
Plan hash value: 1662069396
| Id  | Operation            | Name   | Rows  | Bytes | Cost  |
|   0 | SELECT STATEMENT     |        |   192 |  1344 |     2 |
|   1 |  SORT GROUP BY NOSORT|        |   192 |  1344 |     2 |
|*  2 |   INDEX RANGE SCAN   | T1_IDX |   192 |  1344 |     2 |
Predicate Information (identified by operation id):
   2 - access("A"=1 AND "B">=10 AND "B"<=200)
       filter("A"=1 AND "B">=10 AND "B"<=200)                  ===> *why filter happens here?*
Note
   - cpu costing is off (consider enabling it)Without group by, only access appears in the plan
SQL> select * from  t1 where a=1 and b between 10 and 200 ;
Execution Plan
Plan hash value: 1720721055
| Id  | Operation                   | Name   | Rows  | Bytes | Cost  |
|   0 | SELECT STATEMENT            |        |   192 |  1920 |     3 |
|   1 |  TABLE ACCESS BY INDEX ROWID| T1     |   192 |  1920 |     3 |
|*  2 |   INDEX RANGE SCAN          | T1_IDX |   192 |       |     2 |
Predicate Information (identified by operation id):
   2 - access("A"=1 AND "B">=10 AND "B"<=200)
Note
   - cpu costing is off (consider enabling it)

Answer 1

What's your version ?
No filter on 10.2.0.4 :
SQL> select b,count(*) from t1 where a=1 and b between 10 and 200 group by b;
Execution Plan
Plan hash value: 1662069396
| Id  | Operation            | Name   | Rows  | Bytes | Cost (%CPU)| Time     |
|   0 | SELECT STATEMENT     |        |   192 |  1344 |     2   (0)| 00:00:01 |
|   1 |  SORT GROUP BY NOSORT|        |   192 |  1344 |     2   (0)| 00:00:01 |
|*  2 |   INDEX RANGE SCAN   | T1_IDX |   192 |  1344 |     2   (0)| 00:00:01 |
Predicate Information (identified by operation id):
   2 - access("A"=1 AND "B">=10 AND "B"<=200)
SQL> select * from v$version;
BANNER
Oracle Database 10g Enterprise Edition Release 10.2.0.4.0 - 64bi
PL/SQL Release 10.2.0.4.0 - Production
CORE    10.2.0.4.0      Production
TNS for HPUX: Version 10.2.0.4.0 - Production
NLSRTL Version 10.2.0.4.0 - ProductionNicolas.