Biomolecules, enzyme kinetics

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2014 Q.12)** **1. Governing Concept & Definition**: - **Topic**: Probability & Coin Toss Sequences - Probability that 10 tosses of an unbiased coin all yield identical outcomes (all heads or all tails): $P = \frac{2}{2^{10}} = \frac{2}{1024} = \frac{1}{512} \approx 0.001953 = 1.95 \times 10^{-3}$ Expressed as $K \times 10^{-5} \implies K \approx 195$. **2. Detailed Step-by-Step Calculation**: - Expressed in requested scientific multiplier: $\text{Value} = 195$ **3. Final Answer**: - **Calculated Value**: **195** - **Official GATE Accepted Range**: **191 to 199**