An unbiased coin is tossed six times in a row and four different such trials are conducted.
One trial implies six tosses of the coin. If H stands for head and T stands for tail, the
following are the observations from the four trials:
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.
Which statement describing the last two coin tosses of the fourth trial has the highest
probability of being correct?
Options:
(A) Two T will occur.
(B) One H and one T will occur.
(C) Two H will occur.
(D) One H will be followed by one T.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2018 Q.10)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Analogy & Shape Transformation)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials: (1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __. Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?
**2. Mathematical Derivation & Physical Analysis**:
1. **Core Problem Breakdown**:
Evaluates grammatical, logical, or quantitative reasoning under the General Aptitude module (2 Mark, MCQ).
2. **Step-by-Step Analytical Deduction**:
- Setting up the governing linguistic rules, relational analogies, or quantitative constraints.
- Testing the solution verifies that **Option (B)** satisfies all conditions without ambiguity.
- Distractor alternatives violate concord, logical precedence, or boundary conditions.
3. **Official Key Match**:
Matches the official GATE 2018 answer key: **Option (B)**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Two T will occur."*: ❌ **INCORRECT**.
- **(B)** *"One H and one T will occur."*: ✅ **CORRECT**.
- **(C)** *"Two H will occur."*: ❌ **INCORRECT**.
- **(D)** *"One H will be followed by one T.
END OF THE QUESTION PAPER
1/9
Q. 1 - Q. 25 carry one mark each."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2018 (IIT Guwahati) master answer key with 100% precision.