Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
Three balls, colored in blue, green and red, are successively transferred from
box A to box B in the order BLUE-GREEN-RED. The probability of a reverse
transfer of the balls to the box A in the same order (rounded off to two decimal
places)
is
Official Answer Key:
0.16 - 0.18
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2021 Q.31)**
**1. Governing Concept & Definition**:
- **Topic**: Probability & Permutations without Replacement
- Three distinct colored balls (Blue, Green, Red) transferred successively into Box B in the order Blue $\rightarrow$ Green $\rightarrow$ Red.
- When drawing the three balls back from Box B to Box A one by one without replacement, all permutations of drawing the three distinct balls are equally likely.
**2. Detailed Step-by-Step Calculation**:
- **Total Permutations of 3 distinct balls**:
$n(S) = 3! = 3 \times 2 \times 1 = 6$
- **Favorable Outcomes**:
- Drawing them in the exact same order (Blue first, then Green, then Red): exactly $1$ sequence.
- **Probability Calculation**:
$P = \frac{1}{6} \approx 0.1667 \approx 0.17$
**3. Final Answer**:
- **Calculated Value**: **0.17**
- **Official GATE Accepted Range**: **0.16 to 0.18**
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