Question

A fair coin is tossed 100 times. The probability of getting tails 1 or 3 or 5… …or 49 times is -

• A. ½
• B. ¼
• C. 1/8
• D. 1/16

Answer 1

Answer: (B)

¼

Answer 2

P = = $\frac { X } { 2 ^ { 100 } }$ where X = 2⁹⁸ \ ¹⁰⁰C₀ + ¹⁰⁰C₁ + …… + ¹⁰⁰C₁₀₀ = 2¹⁰⁰

(¹⁰⁰C₀ + ¹⁰⁰C₂ + ….. + ¹⁰⁰C₁₀₀) +(¹⁰⁰C₁+¹⁰⁰C₃ +…+¹⁰⁰C₄₉) + (¹⁰⁰C₅₁ + ¹⁰⁰C₅₃ +….¹⁰⁰C₉₉) = 2¹⁰⁰

2⁹⁹ + [X + X] = 2¹⁰⁰

2⁹⁹ + 2X = 2¹⁰⁰

X = 2⁹⁹ – 2⁹⁸ Ž 2⁹⁸ (2 – 1) = 2⁹⁸

P = 2⁹⁸/2¹⁰⁰ = ¼