Question

Twenty identical coins each with probability $p$ of showing heads are tossed. If the probability of heads showing on $10$ coins is same as that of tails showing on $11$ coins, then $p$ is

• A. $\frac{1}{2}$
• B. $\frac{10}{21}$
• C. $\frac{11}{21}$
• D. $\frac{13}{21}$

Answer 1

The correct option is C $\frac{11}{21}$

The probability of heads showing on $10$ coins $=10p$
The probability of tails showing on $11$ coins $=11(1-p)$
according to question both are same => $10p=11(1-p)$
=> $p=\frac{11}{21}$