🎲 probability

1. **Problem statement:** Find the probability of drawing two kings from a standard deck of 52 cards. 2. **Formula:** Probability of two dependent events both occurring is the prod

1. **Problem statement:** We have a continuous random variable $X$ with probability density function (pdf):

1. **Problem statement:** (i) Given the probability density function (pdf) of a continuous random variable $X$:

1. **Problem statement:** Given the probability density function (pdf) of a continuous random variable $X$:

1. **Problem statement:** The random variable $X$ has a continuous uniform distribution over the interval $[-k, 5k]$ where $k > 0$. We need to find the probability density function

1. **State the problem:** We have a survey table of students categorized by gender and their preferred relaxation method: reading or listening to music. | Gender | Read | Listen to

1. **State the problem:** We are given three probabilities of winning three different games: 0.41, 38%, and 4/10. We need to order these probabilities from least likely to most lik

1. The problem involves understanding conditional probabilities related to email spam detection. 2. We are given:

1. **Problem statement:** We have a spam detection system with the following probabilities:

1. **State the problem:** We have a spam detection system with the following probabilities:

1. **State the problem:** We need to find the probability that a randomly chosen drink order is for cranberry juice. 2. **Identify the total number of drink orders:** Add all the o

1. **Problem statement:** We have three scenarios involving random variables G, H, and Z with different distributions.

1. **Problem statement:** Given a random variable $Y$ with PDF $f(y) = ky^2 e^{-y/4}$ for $y > 0$, find the constant $k$, the CDF $F(y)$, and the probability $P(Y > 8)$. 2. **Find

1. **State the problem:** We need to find the probability of randomly choosing a blue or a yellow sock. 2. **Recall the formula for the union of two events:**

1. **Stating the problem:** We are given the equation $$P(A \cap B) + P(A) + P(B) \times P(A) = 1$$ and the information that events $A$ and $B$ are independent. 2. **Recall the ind

1. **Problem:** Describe the sample spaces for the given situations. 2. **Sample Space Definition:** The sample space is the set of all possible outcomes.

1. **Énoncé du problème :** Soit $X$ une variable aléatoire suivant la loi binomiale de paramètres $n=40$ et $p=0,15$. Nous allons répondre à la question 1 : Combien de chemins don

1. **State the problem:** We roll a 6-sided die and want to find the probability of the event "5 or greater than 3". 2. **Define the events:** Let A = rolling a 5, and B = rolling

1. **State the problem:** You pay 2 dollars to play a game where a fair six-sided die is rolled. You receive a payout equal to the number of dots on the die face. The net gain is t

1. **State the problem:** You pay 2 dollars to play a game where a fair six-sided die is rolled. You receive a payout equal to the number of dots on the die face. The net gain is t

1. **State the problem:** You pay 2 dollars to roll a fair six-sided die. You receive back the number of dollars equal to the number rolled. The net gain (payoff) is the amount rec