<<echo=FALSE, results=hide>>=
## success probability in percent (= pay with card)
p <- sample(15:30, size = 1)

## number of attempts (= customers in queue)
n <- sample(6:9, size = 1)

## minimum number of successes (= customers who pay with card)
k <- sample(1:3, 1)
 
## compute the correct solution in percent
sol <- 100 * pbinom(k - 1, size = n, prob = p/100, lower.tail = FALSE)

ok <- FALSE
while(!ok) {
## two typical errors: 1-p vs. p, pbinom vs. dbinom
err1 <- 100 * pbinom(k - 1, size = n, prob = 1 - p/100, lower.tail = FALSE)
err2 <- 100 * dbinom(k, size = n, prob = p/100)

## two random errors
rand <- runif(2, min = 0, max = 100)

## make sure solutions and errors are unique
ans <- round(c(sol, err1, err2, rand), digits = 2)
ok <- length(unique(ans)) == 5
}
@

\begin{question}
According to a recent survey \Sexpr{100 - p} percent of all customers
in grocery stores pay cash while the rest use their credit or cash card. You
are currently waiting in the queue at the checkout of a grocery story with
\Sexpr{n} customers in front of you.

What is the probability (in percent) that \Sexpr{k} or more of the
other customers pay with their card?

<<echo=FALSE, results=tex>>=
answerlist(ans)
@
\end{question}

\extype{schoice}
\exsolution{10000}
\exname{binomial v3}
\exshuffle{TRUE}