This is an original preparation plan, not a new examination announcement. Check dates, stages, eligibility and application instructions in the issuing authority’s current notice.
01 / UNDERSTANDING
Plan your preparation
Alternate tree diagrams and direct counting so that correct answers come from understanding the experiment rather than memorising one multiplication pattern. State the experiment aloud before writing any favourable-outcome count. For a later review, check the result by counting equally likely ordered selections. Keep a specific error note about keeping the original denominator after drawing without replacement. Use a changed example after a short gap so that remembering one answer does not disguise a remaining misunderstanding.
02 / UNDERSTANDING
The concept in context
Probability compares favourable outcomes with a defined set of possible outcomes when outcomes are equally likely. Drawing a sample space carefully prevents errors about replacement, ordering and the dependence between successive selections. Write the experiment before calculating. For successive draws without replacement, both the available count and the relevant category count may change.
03 / UNDERSTANDING
A worked learning case
A bag contains three blue and two red counters. Two counters are drawn without replacement. The chance that both are blue is three fifths multiplied by two fourths, or three tenths. If the first counter were replaced, the second blue probability would remain three fifths and the final result would instead be nine twenty-fifths.
ORIGINAL EDUCATIONAL PRACTICE
Try it before you check.
What is the probability of drawing one blue followed by one red without replacement?
Show the answer and reasoning
3/10.
The first draw is blue with probability 3/5. Conditional on that event, two red counters remain among four counters, so the next red probability is 2/4. Multiplying gives 6/20, or 3/10. This ordered event excludes the separate outcome red followed by blue, which must be added when order is irrelevant.
Two traps to watch for.
- Keeping the original denominator after drawing without replacement.
- Counting only one order when either colour order is permitted.
YOUR TOPIC-SPECIFIC LEARNING MAP
Build your next study session
Specify whether selections are ordered and whether replacement occurs.
Draw a short probability tree with conditional branch counts.
Check the result by counting equally likely ordered selections.
Explain the idea, apply it to a new situation, then check what changed in your reasoning.
BANKERS TUTORIAL · SOURCE NOTES
Keep the source alongside your notes.
Official links provide subject context and authoritative reference material. This guide’s explanation, scenario and question are original Bankers Tutorial learning content.
- www.ibps.in https://www.ibps.in/wp-content/uploads/Detailed-Notification_CRP-PO-XIV_7.8.24.pdf
For IBPS & RRB preparation, check the current official notice before relying on changing dates, rules or examination requirements.
