This is an independent topic guide, not the official syllabus. Compare it with the current paper outline and rules published by the examination authority.
01 / UNDERSTANDING
Learning objectives
Cover complements, conditional events, mutually exclusive outcomes and independence, using small sample spaces before applying compact formulas to larger counts. Compare both-colour outcomes with one specified colour order in a sample tree. Your practical tasks are to specify whether selections are ordered and whether replacement occurs and draw a short probability tree with conditional branch counts. These conceptual objectives are a study framework, not an official question allocation. Demonstrate the distinction with a fresh worked case, including the assumptions that make the answer valid.
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
Your revision map
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.
