🎲 probability

1. **Stating the problem:** We want to predict the next set of 6 numbers for Lottotech and Loto Plus based on past draws using mathematical probability. 2. **Understanding the prob

1. **State the problem:** We want to find the probability that a message containing the word "Rolex" is spam. 2. **Given data:**

1. **Problem Statement:** We have three independent events A, B, and C representing hits by three guns with probabilities $P(A)=0.5$, $P(B)=0.6$, and $P(C)=0.8$. We want to find:

1. The problem is to find the probability of playing tennis, denoted as $P(\text{tennis})$. 2. The formula for probability is:

1. The problem is to find the probability of an event, specifically the probability of playing tennis, denoted as $P(\text{tennis})$. 2. The formula for probability is:

1. The problem is to understand the moment generating function (MGF) and raw moments. 2. The moment generating function $M_X(t)$ of a random variable $X$ is defined as:

1. The problem is to find the probability $p(X)$ of a random variable $X$. 2. The formula to find $p(X)$ depends on the context: if $X$ is discrete, $p(X=x)$ is the probability mas

1. Problem: A couple plans to have three children. We assume each child is equally likely to be a boy or a girl with probability $\frac{1}{2}$ independently. Formula: For $n$ indep

1. Problem: A couple plans to have three children. Find the probabilities for different gender combinations. 2. Formula: For independent events, probability of a specific outcome i

1. **State the problem:** We have a discrete probability distribution with values $x = \{1, 2, 3, 4, 5\}$ and probabilities $p(x) = \left\{\frac{1}{9}, \frac{2}{9}, \frac{1}{3}, \f

1. **State the problem:** We have 11 students in total. The Chess Club members are Aldo, Latoya, Yolanda, Melissa (4 students). The Science Club members are Sam, Goran, Latoya, Ann

1. **Problem Statement:** We have a group of 7 spectators randomly selected from a crowd where 70% are males. We want to find:

1. **State the problem:** We want to find the experimental probability that a randomly selected vehicle is not blue. 2. **Recall the formula for experimental probability:**

1. **State the problem:** We need to find the probability that an event will occur based on experimental data, and then find the probability that the event will not occur using the

1. **Problem statement:** We have a discrete random variable $X$ with probability mass function (pmf) given by $$P(X=x) = \frac{x+1}{m}, \quad x = 1,2,3,4,5,6.$$ We need to find: i

1. **Problem statement:** We have 5 identical cards numbered 2, 3, 4, 5, 6. Two cards are drawn one after the other with replacement, forming a two-digit number. We want to find th

1. **Problem statement:** We have 8 cards numbered 1 to 8. Two cards are drawn successively with replacement. We want to find the probability that the absolute difference between t

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

1. **Problem Statement:** Determine whether the given distribution is a valid probability distribution for a discrete random variable $X$ with values $5, 6, 7, 4$ and probabilities

1. **Problem Statement:** Given the probability density function (pdf) $f(x) = 3x^2$ for $0 \leq x \leq 1$, find values of $a$ and $b$ such that: i) $P(X \leq a) = P(X > b) = 0.05$

1. **State the problem:** We want to find the probability that a randomly chosen customer who ordered a dessert did not order a starter. 2. **Identify the sets and numbers:**