Question

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing 50 coins is equal to that head showing 51 coins, then the value of p is

• A. $\frac{1}{2}$
• B. $\frac{49}{101}$
• C. $\frac{50}{101}$
• D. $\frac{51}{101}$

Answer 1

The correct option is D $\frac{51}{101}$

Let P1 and P2 be the respectively be the probability of heads showing 50 coins and head showing 51 coins $P_1=100C_{50}{p}^{50}(1-p{)}^{50}and{P}_2=100C_{51}{p}^{51}(1-p{)}^{49}$
$Given{P}_1=P_2$
$\Rightarrow 100C_{50}{p}^{50}(1-p{)}^{50}=100C_{51}{p}^{51}(1-p{)}^{49}$
$\Rightarrow \frac{1-p}{p}=\frac{50}{51}\Rightarrow p=\frac{51}{101}.$