The worked question on this page is original educational practice. It is not represented as a question from an official previous-year examination paper.
01 / UNDERSTANDING
Review the question
Invent a small coloured-counter experiment and solve it with both a tree and combinations, explicitly stating whether the answer depends on order. Adding replacement changes the second denominator and can change event dependence. An original checkpoint is: What is the probability of drawing one blue followed by one red without replacement? Supported answer: 3/10. Explain the decisive fact, then alter one condition and solve again. This is an original practice method, not a claim that the question appeared in an official past paper.
02 / UNDERSTANDING
The concept in context
The formula favourable divided by total needs equally likely elementary outcomes. Counting labels carelessly can give different weights to outcomes that should not be treated alike. A useful study check is to specify whether selections are ordered and whether replacement occurs, then check the result by counting equally likely ordered selections. Explain why the method fits the stated facts before applying it to a changed situation.
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
Learn from the attempt
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.
