Question

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to getting 9 heads, then the probability of getting 2 heads is,

• A. 15/2⁸
• B. 2/15
• C. 15/2¹³
• D. None of these

Answer 1

Answer: (C)

15/2¹³

Answer 2

Let coin was tossed 'n' times and X be the random variable representing the number of head appearing in 'n' trials.

P(X = 7) = P (X = 9) ⇒ ⁿ C₇(1/2)⁷ (1/2)^n–7

= ⁿC₉(1/2)^n–9 × (1/2)⁹

⇒ ⁿC₇ = ⁿC₉ ⇒ n = 16

Now P (X = 2) = ¹⁶C₂(1/2)² (1/2)¹⁴ = = $\frac { 15 } { 2 ^ { 13 } }$