Riigieksamid (Estonian State Exams) · Mathematics

Probability, Combinatorics and Statistics

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

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A committee of 3 members is to be chosen at random from 5 men and 4 women. What is the probability that the committee consists of 2 men and 1 woman?
How many distinct 5-letter permutations can be formed using the letters of the word LEVEL?
In a binomial experiment with $n = 4$ independent trials and success probability $p = 0.25$ , what is the probability of obtaining at least one success?
What is the variance $σ^{2}$ of the discrete uniform distribution over the set ${1, 2, 3, 4, 5}$ ?
Events $A$ and $B$ satisfy $P (A) = 0.4$ , $P (B) = 0.5$ , and $P (A \cup B) = 0.7$ . What is the conditional probability $P (A ∣ B)$ ?
Two fair standard 6-sided dice are rolled simultaneously. What is the probability that the sum of the numbers is 8?
A discrete random variable $X$ takes values 1, 2, and 3 with probabilities $P (X = 1) = 0.2$ , $P (X = 2) = 0.5$ , and $P (X = 3) = 0.3$ . What is its expected value $E (X)$ ?
In how many ways can 6 people be seated around a circular dinner table where rotations are considered equivalent?
If random variable $X \sim N (μ, σ^{2})$ is standard normally distributed, what is $P (- 1.96 \leq Z \leq 1.96)$ to the nearest whole percentage?
A box contains 3 defective lightbulbs and 7 non-defective lightbulbs. Two bulbs are drawn at random without replacement. What is the probability of drawing at least one defective bulb?

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