GATE AG 2015 • Q38 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: Thermodynamic principles of I.C. engines

Question Statement:

A coin is tossed ten times. The probability of getting five heads and five tails is _____.

Official Answer Key:

0.23 to 0.26

Step-by-Step Solution & Explanation

Number of heads in 10 tosses follows a Binomial distribution with n=10, p=0.5. P(X=5) = C(10,5)×(0.5)⁵×(0.5)⁵ = 252 × 0.5¹⁰ = 252/1024 = 0.2461. This lies within the accepted range 0.23–0.26.

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