VWO / HAVO Centraal Examen (Netherlands) · Mathematics

Probability, Combinatorics and Statistics

11 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 11 questions

A standard fair six-sided die is rolled 4 times. What is the probability of obtaining at least one six?
In a class of 30 students, 18 take physics, 15 take chemistry, and 8 take both subjects. What is the probability that a randomly chosen student takes neither physics nor chemistry?
What is the variance of a random variable $X$ that follows a binomial distribution with $n = 50$ trials and success probability $p = 0.4$ ?
How many distinct 4-digit PIN codes can be formed using the digits 0 to 9 if no digit may be repeated?
A medical diagnostic test has a $98%$ sensitivity (true positive rate) and a $95%$ specificity (true negative rate). If the disease prevalence is $1%$ , what is the probability that a person who tes…
What is the median of the data set: $4, 8, 3, 12, 15, 7, 9, 2, 10$ ?
If the correlation coefficient between two variables $X$ and $Y$ is $r = - 0.85$ , how should this relationship be interpreted?
In a continuous probability density function $f (x) = k x$ defined on the interval $[0, 4]$ , what must the value of the constant $k$ be for $f (x)$ to be a valid probability density function?
What happens to the margin of error of a confidence interval for a population mean when the sample size $n$ is quadrupled (multiplied by 4), holding confidence level constant?
Two cards are drawn sequentially without replacement from a standard well-shuffled 52-card deck. What is the probability that both cards are Aces?
Under a two-tailed hypothesis test with significance level $α = 0.05$ , what is the critical z-value threshold for rejecting the null hypothesis?

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