Question

Nupur and Sheetal play a game "eight time coin throw”. If the fair coin shows heads, Nupur gets a point & if it shows tails, Sheetal gets a point. After eight throws, they compare their scores. What is the probability that the game will be a tie?

• A. $\frac{1}{8}$
• B. $\frac{1}{9}$
• C. $\frac{35}{128}$
• D. $\frac{33}{128}$

Answer 1

The correct option is C $\frac{35}{128}$

For a tie, there would be 4 heads and 4 tails.

Probability of "4” heads in 8 throws can be found using ${}^n$C${}_r$ p${}^r$ q${}^{n-r}$ = ${}^8$C${}_4$ ${\left(\frac{1}{2}\right)}^4$ ${\left(\frac{1}{2}\right)}^4$ = $\frac{35}{128}$