A fair coin is tossed a fixed number of times. If the probability of

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

Options:

A . 35212

B . 35214

C . 7212

D . 7214

Answer: Option A
:
A
Probability of r successes in n trials is equal to

^{n} C_{r} p^{r} q^{n - r}

, where p is the probability of success in one trial and q is the probability of failure in one trial.
Let the coin be tossed n times. Here p and q are both 1/2

P (g e t t i n g 7 h e a d s) = n C_{7} {(\frac{1}{2})}^{n} a n d P (g e t t i n g 9 h e a d s) = n C_{9} {(\frac{1}{2})}^{n} G i v e n, P (7 h e a d s) = P (9 h e a d s) \Rightarrow n C_{7} = n C_{9} \Rightarrow n = 16 ∴ P (3 h e a d s) = 16 C_{3} {(\frac{1}{2})}^{16} = \frac{35}{2^{12}} .

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