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

Using the binomial probability formula, the probability of exactly 10 heads is 20C10 multiplied by p^10 multiplied by (1-p)^10, and the probability of exactly 11 tails is 20C11 multiplied by p^9 multiplied by (1-p)^11. Setting these two equal and simplifying gives p divided by (1-p) equals 11 divided by 10. Solving this equation yields p = 11/21.

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