German Abitur · Mathematics

Probability and Statistics

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

Practise Probability and Statistics now

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

All 19 questions

A fair die is rolled once. What is the probability of an even number?
If $P (A) = 0.35$ , what is $P (\overset{ˉ}{A})$ , the probability of the opposite event?
A fair die is rolled twice. What is the probability of at least one six?
A fair coin is tossed $3$ times. What is the probability of exactly two heads?
What is the expected value of one roll of a fair die?
Given $P (A) = 0.3$ and $P (B ∣ A) = 0.5$ , what is $P (A \cap B)$ ?
A disease affects $1 %$ of a population. A test detects it in $90 %$ of the sick people and wrongly reacts in $5 %$ of healthy people. What is the probability that a person with a positive test…
In how many ways can $4$ different books be arranged on a shelf?
What is $(2 5)$ ?
A random variable $X$ is binomial with $n = 10$ and $p = 0.2$ . What is its standard deviation?
For independent events with $P (A) = 0.4$ and $P (B) = 0.5$ , what is $P (A \cup B)$ ?
An urn holds $3$ red and $2$ blue balls. Two balls are drawn without replacement. What is the probability that both are red?
What is the mean of the data $2, 4, 6, 8$ ?
What is the median of the data $3, 9, 1, 7, 5$ ?
A fair die is rolled $n$ times. What is the smallest $n$ for which the probability of at least one six exceeds $90 %$ ?
A random variable X is binomial with n = 3 and p = 1/3. What is P(X = 1)?
A random variable X is binomial with n = 3 and p = 1/2. What is P(X = 2)?
A random variable X is binomial with n = 4 and p = 1/2. What is P(X = 2)?
A random variable X is binomial with n = 6 and p = 1/2. What is P(X = 3)?

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