A release-checked easy problem for training Discrete Random Variables.
Question
Brad and Chad both flip coins with probability $p$ of heads on each flip. Let $B$ be the event that it takes strictly less flips for Brad to get his first heads than Chad, $C$ be the event that it takes Chad strictly less flips than Brad to get his first heads than Brad, and $E$ be the event that it takes them an equal number of flips to obtain their first heads. Find the value of $p$ such that $\mathbb{P}[E] = \mathbb{P}[C]$.
Practice focus
This Probability problem is tagged Discrete Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.