Question

One hundred identical coins each with probability p as showing up heads are tossed. If $0<p<1$ and the probability of heads showing on 50 coins is equal to that of heads on 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 x be the number of coins showing heads

Given $P(x=50)=P(x=51)$ and the probability of a coin showing head is p.

For $P(x=50)$ ,out of 100 coins,50 are to be selected ,which means ${}_{50}^{100}C$. The probability that these 50 coins are to be selected which means

${}_{50}^{100}C$

The probability of other 50 coins showing up tail is ${(1-p)}^{50}$

$\frac{p}{1-p}=\frac{51}{50}\Rightarrow p=\frac{51}{101}$