optimizer always full scans table eben though fething only 3 rows - oracle

Question

I have a table foo which was created like this.
CREATE TABLE foo AS SELECT * FROM all_objects;
CREATE INDEX foo_I1 ON foo(owner,object_type,status);
exec dbms_stats.gather_table_stats('hr','foo',method_opt=>'FOR ALL COLUMNS size AUTO');
I created an index on 3 columns and firing a query which looks like below.
select * from foo where status='INVALID';
select * from foo where status='VALID';
status='VALID' fetches near about 71000 rows in a table of 71780 rows. it does a full table scan. it's understandable. but in case of status='INVALID' which fetches only 3 rows , it's doing full table scan. It's also getting A rows and E rows very different.
PLAN: same for both queries.
SQL_ID gdhy9j91gu9sm, child number 0
select /*+gather_plan_statistics */ * from foo where status='VALID'
Plan hash value: 1245013993
------------------------------------------------------------------------------------
| Id | Operation | Name | Starts | E-Rows | A-Rows | A-Time | Buffers |
------------------------------------------------------------------------------------
| 0 | SELECT STATEMENT | | 1 | | 50 |00:00:00.01 | 4 |
|* 1 | TABLE ACCESS FULL| FOO | 1 | 71773 | 50 |00:00:00.01 | 4 |
------------------------------------------------------------------------------------
Predicate Information (identified by operation id):
---------------------------------------------------
1 - filter("STATUS"='VALID')
Please explan this behaviour. Database Version: 11.2g oracle.

Answer 1

A missing histogram is probably causing the full table scan. Histograms are usually only created if the data is skewed and if the column has been used in a relevant predicate.
Sometimes you need to run a query before gathering statistics, to let Oracle know that this column is important enough to deserve a histogram.
select * from foo where status='INVALID';
exec dbms_stats.gather_table_stats('hr','foo',method_opt=>'FOR ALL COLUMNS size AUTO');
Re-run the SELECT and now it can use the histogram. With the histogram Oracle knows that INVALID returns a small number of rows, and an index would be useful:
explain plan for select * from foo where status='INVALID';
select * from table(dbms_xplan.display);
Plan hash value: 1520589999
---------------------------------------------------------------------------------------------
| Id | Operation | Name | Rows | Bytes | Cost (%CPU)| Time |
---------------------------------------------------------------------------------------------
| 0 | SELECT STATEMENT | | 1 | 134 | 217 (0)| 00:00:01|
| 1 | TABLE ACCESS BY INDEX ROWID BATCHED| FOO | 1 | 134 | 217 (0)| 00:00:01|
|* 2 | INDEX SKIP SCAN | FOO_I1 | 1 | | 216 (0)| 00:00:01|
---------------------------------------------------------------------------------------------
Predicate Information (identified by operation id):
---------------------------------------------------
2 - access("STATUS"='INVALID')
filter("STATUS"='INVALID')