🎲 probability

1. **Problem statement:** Find the probability that a student passes the statistics test given:

1. **State the problem:** We have two plants producing parts. Plant 1 produces 1500 parts with 150 defective, and Plant 2 produces 2800 parts with 260 defective. A part is randomly

1. **Problem statement:** A company has three plants producing 50%, 30%, and 20% of relays. The probabilities of a relay being defective from these plants are 0.02, 0.05, and 0.01

1. **Problem statement:** Given the probability density function (pdf) of a continuous random variable $Y$: $$f(y) = \begin{cases} \frac{1}{5}, & 0 \leq y < 2 \\ \frac{1}{2}y + D,

1. Let's start by stating the problem: We want to find the moments of a random variable $X$. 2. The $n$-th moment of a random variable $X$ is defined as $E[X^n]$, which is the expe

1. **State the problem:** We want to find the probability of having at most 2 rainy days in 5 days, given each day has a 40% chance of rain. 2. **Identify the distribution:** This

1. **Stating the problem:** Construct a real-world situation involving counting techniques and probability, identify the techniques to use, and solve the problem.

1. **Problem 50:** Determine which given set of probabilities cannot be a discrete probability distribution. 2. **Recall the rules for a discrete probability distribution:**

1. The problem is to find the probability density function (PDF) of a continuous random variable. 2. The PDF is a function that describes the likelihood of a random variable to tak

1. **Problem (a):** Find the probability of picking a pencil that is red or yellow. 2. The probability of picking a pencil of each colour is given as:

1. **Énoncé du problème :** Une urne contient 10 boules indiscernables au toucher, dont 4 portent le chiffre 1 et 6 portent le chiffre 5. On tire simultanément deux boules.

1. **Problem statement:** Alex has a 10-faced die with faces 1 to 10. The probability of each face is proportional to its number, so probabilities are in ratio $1:2:3:4:5:6:7:8:9:1

1. **Problem statement:** Develop a formula for a random variate generator for a random variable $X$ with p.d.f. $$f(x) = \begin{cases} e^{2x} & -\infty < x \leq 0 \\ e^{-2x} & 0 <

1. The problem is to decide how to start a tree diagram for a scenario involving regular exercise and no exercise or regular breakfast and no breakfast. 2. A tree diagram is a visu

1. **Problem statement:** A group of office workers were surveyed. Given:

1. დავწეროთ მოცემული პირობა: ერთი ცდის შედეგად ხდომილობის მოხდენის ალბათობა არის $p$. სამი დამოუკიდებელი ცდის შედეგად ამ ხდომილობის ზუსტად 1-ჯერ მოხდენის ალბათობა არის $P(X=1)$ და

1. **Problem Statement:** A bag contains 3 white, 4 black, and 5 blue balls (total 12 balls). Four balls are drawn. Find the probability that the drawn balls are 2 white, 1 black,

1. Énoncé du problème : Soit $X$ une variable aléatoire réelle sur un espace probabilisé fini. Montrer que $$E(X)^2 \leq E(X^2)$$. 2. Formule utilisée : On utilise l'inégalité de C

1. Let's start by stating the problem: What is a distribution function? 2. A distribution function, often called a cumulative distribution function (CDF), describes the probability

1. **Stating the problem:** We want to understand what random variables are, their types, and see examples with solutions. 2. **Definition:** A random variable is a function that a

1. The problem is to understand what random variables are. 2. A random variable is a function that assigns a numerical value to each outcome in a sample space of a random experimen