```{r data generation, 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
}
```
Question
========
According to a recent survey `r 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
`r n` customers in front of you.
What is the probability (in percent) that `r k` or more of the
other customers pay with their card?
```{r questionlist, echo = FALSE, results = "asis"}
answerlist(ans, markup = "markdown")
```
Meta-information
================
extype: schoice
exsolution: 10000
exname: binomial v3
exshuffle: TRUE