On a tennis court, a ball launcher allows a player to train alone. This device sends balls one by one at a regular rate. The player then hits the ball and the next ball arrives. According to the manufacturer's manual, the ball launcher sends the ball randomly to the right or to the left with equal probability.

Throughout the exercise, results will be rounded to $10 ^ { - 3 }$ near.

\section*{Part A}
The player is about to receive a series of 20 balls.

\begin{enumerate}
  \item What is the probability that the ball launcher sends 10 balls to the right?
  \item What is the probability that the ball launcher sends between 5 and 10 balls to the right?
\end{enumerate}

\section*{Part B}
The ball launcher is equipped with a reservoir that can hold 100 balls. Over a sequence of 100 launches, 42 balls were launched to the right.\\
The player then doubts the proper functioning of the device. Are his doubts justified?

\section*{Part C}
To increase the difficulty, the player configures the ball launcher to give spin to the balls launched. They can be either ``topspin'' or ``slice''. The probability that the ball launcher sends a ball to the right is still equal to the probability that the ball launcher sends a ball to the left.\\
The device settings allow us to state that:

\begin{itemize}
  \item the probability that the ball launcher sends a topspin ball to the right is 0.24;
  \item the probability that the ball launcher sends a slice ball to the left is 0.235.
\end{itemize}

If the ball launcher sends a slice ball, what is the probability that it is sent to the right?