🎲 probability

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:**

1. **Énoncé du problème :** On considère une variable aléatoire $X$ suivant une loi du Khi-deux avec $k=4$ degrés de liberté.

1. ปัญหาคือ ต้องการหาความน่าจะเป็นที่จะสุ่มนิสิต 5 คน จากนิสิตทั้งหมด 16 คน โดยที่ได้นิสิตชายอย่างมาก 2 คน 2. สูตรความน่าจะเป็นสำหรับการเลือกแบบไม่เรียงลำดับคือ

1. ปัญหาคือการหาค่าคาดหวัง (Expected Value) และความแปรปรวน (Variance) ของตัวแปรสุ่ม X 2. สูตรค่าคาดหวังคือ $$E(X) = \sum xP(x)$$ ซึ่งเป็นผลรวมของค่าตัวแปรคูณกับความน่าจะเป็นของแต่ล

1. The problem is to find the expected value $E(X)$ and the variance $\mathrm{Var}(X)$ of a random variable $X$ given its probability distribution. 2. The expected value formula is

1. **Problem statement:** We have two real numbers $x, y$ chosen randomly from the interval $[0,1]$.

1. **State the problem:** We have 6 batteries in total, 2 of which are defective. We select 2 batteries at random without replacement. We want to find the probability that both sel

1. **Stating the problem:** We want to find the probability that a participant wins the game.

1. **State the problem:** We are given probabilities $P(A_1)=0.58$, $P(A_2)=0.34$, and $P(A_1 \cap A_2)=0.09$. We want to find the probability that at least one of the two diagnose

1. **Problem statement:** We have a binomial random variable $X \sim \text{Binomial}(n=5, p=0.55)$ and want to find the probability $P(X \leq 2)$, which means the probability that

1. **State the problem:** Given probabilities $P(A)=0.792$, $P(B)=0.538$, $P(C)=0.783$, and intersections $P(A \cap B)=0.394$, $P(A \cap C)=0.589$, we want to understand these valu

1. مسئله: مجموعه $A = \{-1, 3, 5, 7, 9, 11\}$ داده شده است. باید احتمال انتخاب تصادفی زیرمجموعه‌ای از $A$ را پیدا کنیم که حاصل ضرب بزرگترین و کوچکترین عضو آن برابر با 7 باشد. 2. اب

1. مسئله: مجموعه $A = \{-13, 5, 7, 9, 11\}$ داده شده است. می‌خواهیم احتمال انتخاب تصادفی زیرمجموعه‌ای از $A$ را که حاصل جمع بزرگترین و کوچکترین عضو آن برابر 7 باشد، پیدا کنیم. 2. ا

1. **State the problem:** We have a spinner with three colored sections: blue, yellow, and pink. It was spun 100 times. 2. **Given data:**

1. **Problem Statement:** We have two boxes: Box 1 contains numbers 3, 5, 8 and Box 2 contains numbers 4, 7. One slip is taken from each box.

1. **Problem 3:** Given events A, B, and C with $$P(A) = \frac{1}{2}, \quad P(C) = \frac{1}{2}, \quad P(A \cup B) = \frac{5}{8}$$

1. **Problem Statement:** What is the probability of an impossible event?

1. **Problem Statement:** We are testing 3 cellphones and want to find the probability distribution of the random variable $x$, which represents the number of defective cellphones.

1. **Problem Statement:** We are testing 3 cellphones and want to find the probability distribution of the random variable $x$, which represents the number of defective cellphones.

1. **Problem Statement:** We have two random variables:

1. **Problem statement:** Given two independent events $A$ and $B$ in sample space $\Omega$ with $P(A \cap B) = 0.08$ and $P(A) = 2P(B)$, find $P(A \cup B)$.