SQL> desc t
 Name                                      Null?    Type
 ----------------------------------------- -------- ----------------------------
 OWNER                                              VARCHAR2(30)
 NAME                                               VARCHAR2(30)
 TYPE                                               VARCHAR2(12)
 LINE                                               NUMBER
 TEXT                                               VARCHAR2(4000)

SQL> create index t_idx on t(owner);

Index created.

SQL> analyze table t compute statistics;

Table analyzed.

SQL> set autotrace on explain
SQL> select count(*) from t where owner='NOBODY';

  COUNT(*)
----------
         0

Execution Plan
----------------------------------------------------------
   0      SELECT STATEMENT Optimizer=CHOOSE (Cost=19 Card=1 Bytes=5)
   1    0   SORT (AGGREGATE)
   2    1     INDEX (RANGE SCAN) OF 'T_IDX' (NON-UNIQUE) (Cost=19 Card
          =8134 Bytes=40670)

-- as seen above, count(*) needs to scan only the index

SQL> select owner from t where owner='NOBODY';

no rows selected

Execution Plan
----------------------------------------------------------
   0      SELECT STATEMENT Optimizer=CHOOSE (Cost=19 Card=8134 Bytes=4
          0670)

   1    0   INDEX (RANGE SCAN) OF 'T_IDX' (NON-UNIQUE) (Cost=19 Card=8
          134 Bytes=40670)

-- again ,it needs to scan only the index ,becos you are selecting the indexed column and nothing else

SQL> select NAME from t where owner='NOBODY';

no rows selected

Execution Plan
----------------------------------------------------------
   0      SELECT STATEMENT Optimizer=CHOOSE (Cost=689 Card=8134 Bytes=
          138278)

   1    0   TABLE ACCESS (BY INDEX ROWID) OF 'T' (Cost=689 Card=8134 B
          ytes=138278)

   2    1     INDEX (RANGE SCAN) OF 'T_IDX' (NON-UNIQUE) (Cost=19 Card
          =8134)

-- here it needs to access the TABLE data after scanning the index.  But if I alter db_file_multiblock_read_count ,like this 

SQL> alter session set db_file_multiblock_read_count=256;

Session altered.

-- and retry the same select, I get a full table scan!

SQL> select NAME from t where owner='NOBODY';

no rows selected

Execution Plan
----------------------------------------------------------
   0      SELECT STATEMENT Optimizer=CHOOSE (Cost=317 Card=8134 Bytes=
          138278)

   1    0   TABLE ACCESS (FULL) OF 'T' (Cost=317 Card=8134 Bytes=13827
          8)

-- So you see, the CBO will prefer to use a full table scan when its associated cost is estimated to be lower than the index scan.

-- Reducing it back

SQL>alter session set db_file_multiblock_read_count=32;

Session altered.

SQL> select * from t where owner='NOBODY';

no rows selected

Execution Plan
----------------------------------------------------------
   0      SELECT STATEMENT Optimizer=CHOOSE (Cost=689 Card=8134 Bytes=
          2952642)

   1    0   TABLE ACCESS (BY INDEX ROWID) OF 'T' (Cost=689 Card=8134 B
          ytes=2952642)

   2    1     INDEX (RANGE SCAN) OF 'T_IDX' (NON-UNIQUE) (Cost=19 Card
          =8134)

-- create a concatenated index on NAME,OWNER to make use of INDEX FULL SCAN

SQL> create index t_idx2 on t(name,owner);

Index created.

SQL> analyze table t compute statistics;

Table analyzed.

SQL> select NAME from t where owner='NOBODY';

no rows selected

Execution Plan
----------------------------------------------------------
   0      SELECT STATEMENT Optimizer=CHOOSE (Cost=60 Card=8134 Bytes=1
          38278)

   1    0   INDEX (FAST FULL SCAN) OF 'T_IDX2' (NON-UNIQUE) (Cost=60 C
          ard=8134 Bytes=138278)

-- I know Index Fast full scan was introduced in 7.3, but sometimes need an explicit hint to use it.