Question

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

• A. $1/64$
• B. $1/32$
• C. $1/16$
• D. $1/8$

Answer 1

Answer: (B)

$1/32$

Let, the fixed number is $n$.
So, ${}^n{c}_3{=}^n{c}_5\Rightarrow n=8$
Thus, required probability is ${}^8{c}_1\times {\left(\frac{1}{2}\right)}^8=\frac{1}{32}$