Question

If a coin is tossed a fixed number of times, the probability of getting 6 heads is equal to the probability of getting 8 heads. Find the number of times the coin was tossed.

• A. $12$
• B. $13$
• C. $14$
• D. $15$

Answer 1

Answer: (C)

$14$

Given: A coin tossed $n$ times, P(getting 6 heads)=P(getting 8 heads)

To find: the number of times the coin was tossed

If we toss a fair coin $n$ number of times, then using Binomial we can write

The probability of getting 6 heads =${}^n{C}_6{\left(\frac{1}{2}\right)}^n$

The probability of getting 8 heads = ${}^n{C}_8{\left(\frac{1}{2}\right)}^n$

According to the question,

${}^n{C}_6{\left(\frac{1}{2}\right)}^n{=}^n{C}_8{\left(\frac{1}{2}\right)}^n⟹{}^n{C}_6{=}^n{C}_8⟹\frac{n!}{6!(n-6)!}=\frac{n!}{8!(n-8)!}⟹8\times 7=(n-6)(n-7)⟹n^2-13n+42-56=0⟹n^2-13n-14=0$

$⟹n^2-14n+n-14=0⟹(n-14)(n+1)=0$

$⟹n=14$ as n cannot be negative.