Question

A fair coin is tossed n times. if the probability that head occurs $6$ times is equal to the probability that head occurs $8$ times, then value of $n$ is

• A. $24$
• B. $48$
• C. $14$
• D. $16$

Answer 1

Answer: (C)

$14$

Let X be the number of times head occurs. Then X follows a binomial
distribution with parameter n and $p=1/2$.
We are given that, $P(X=6)=P(X=8)$.
${\Rightarrow }^n{C}_6{\left(\frac{1}{2}\right)}^6{\left(\frac{1}{2}\right)}^{n-6}{=}^n{C}_8{\left(\frac{1}{2}\right)}^8{\left(\frac{1}{2}\right)}^{n-8}$
${\Rightarrow }^n{C}_6{\left(\frac{1}{2}\right)}^n{=}^n{C}_8{\left(\frac{1}{2}\right)}^n$
${\Rightarrow }^n{C}_6{=}^n{C}_8{=}^n{C}_{n-8}\Rightarrow 6=n-8$ or $n=14$