Question

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that of getting 9 heads, then the probability of getting 3 heads is

• A. 35/2¹²
• B. 35/2¹⁴
• C. 7/2¹²
• D. None of these

Answer 1

Answer: (A)

35/2¹²

Answer 2

Let the coin be tossed n times

P(7 heads) = $nC_{7}\left( \frac{1}{2} \right)^{7}\left( \frac{1}{2} \right)^{n - 7} =^{n}C_{7}\left( \frac{1}{2} \right)^{n}$

And P(9 heads) = $nC_{9}\left( \frac{1}{2} \right)^{9}\left( \frac{1}{2} \right)^{n - 9} =^{n}C_{9}\left( \frac{1}{2} \right)^{n}$

P(7 heads) = P(9 heads) ⇒ $nC_{7} =^{n}C_{9} \Rightarrow n = 16$.

∴ P(3 heads) = $16C_{3}\left( \frac{1}{2} \right)^{3}\left( \frac{1}{2} \right)^{16 - 3} =^{16}C_{2}\left( \frac{1}{2} \right)^{16} = \frac{35}{2^{12}}$