On a given day, an automatic checkout triggers 15 checks. The probability that a check reveals an error is $p = 0.165$. The detection of an error during a check is independent of other checks. We denote $X$ the random variable equal to the number of errors detected during the checks on this day.
We admit that the random variable $X$ follows a binomial distribution. Specify its parameters.
Determine the probability that exactly 5 errors are detected. The answer will be given rounded to the nearest hundredth.
Determine the probability that at least one error is detected. The answer will be given rounded to the nearest hundredth.
We wish to modify the number of checks triggered by the checkout so that the probability that at least one error is detected each day is greater than $99\%$. Determine the number of checks that the checkout must trigger each day for this constraint to be satisfied.
On a given day, an automatic checkout triggers 15 checks. The probability that a check reveals an error is $p = 0.165$. The detection of an error during a check is independent of other checks.\\
We denote $X$ the random variable equal to the number of errors detected during the checks on this day.
\begin{enumerate}
\item We admit that the random variable $X$ follows a binomial distribution. Specify its parameters.
\item Determine the probability that exactly 5 errors are detected. The answer will be given rounded to the nearest hundredth.
\item Determine the probability that at least one error is detected. The answer will be given rounded to the nearest hundredth.
\item We wish to modify the number of checks triggered by the checkout so that the probability that at least one error is detected each day is greater than $99\%$. Determine the number of checks that the checkout must trigger each day for this constraint to be satisfied.
\end{enumerate}