Question

A coin is tossed $n$ times. If the probability of getting head $6$ times is equal to the probability of getting head 8 times then $n=$

• A. $6$
• B. $8$
• C. $14$
• D. $10$

Answer 1

Answer: (C)

$14$

Probability of getting heads exactly 6 times in n tosses of a coin
$=n{C}_6.\frac{1}{2^n}$.
Probability of getting heads exactly 8 times in n tosses of a coin
$=n{C}_8.\frac{1}{2^n}$.
It is given that both are equal.
Hence
$n{C}_6.\frac{1}{2^n}=n{C}_8.\frac{1}{2^n}$
Or
${}^n{C}_6={}^n{C}_8$
Or
${}^n{C}_{n-6}={}^n{C}_8$
$n-6=8$
$n=14$.
Hence no of trials are 14.