🎲 probability

1. Let's start by stating the problem: We want to understand the binomial distribution, which helps us find the probability of getting a certain number of successes in a fixed numb

1. مسئله را بیان می‌کنیم: در یک خانواده سه فرزندی، جنسیت هر فرزند می‌تواند پسر (P) یا دختر (D) باشد. 2. فضای نمونه شامل تمام ترکیبات ممکن جنسیت سه فرزند است:

1. The problem is to analyze the probability of landing on certain numbers on the Dream Catcher wheel and understand the game mechanics. 2. The wheel has segments with different va

1. نبدأ بحل التمرين 1. 2. **بيان المشكلة:** لدينا صندوق يحتوي على 4 كرات بيضاء، 3 كرات سوداء، و2 كرتين حمراوين. نسحب كرتين في آن واحد.

1. مسئله را بیان می‌کنیم: تابع احتمال گسسته $f_X(x) = \frac{1}{4}$ برای مقادیر $x = 0, 1, 2, 3$ داده شده است. هدف بررسی صحت تابع احتمال و محاسبه مقادیر مرتبط است. 2. فرمول تابع احت

1. ננסח את הבעיה: בכיתה יש 8 תלמידים ו-9 תלמידות, סך הכל 17 תלמידים. מוציאים אדם אחד מהכיתה. אם זה בת, משאירים אותה בחוץ. אם זה בן, מכניסים אחת במקומו. לאחר מכן מוציאים שוב אדם מהכ

1. **הבעיה:** בכיתה יש 8 תלמידים ו-9 תלמידות. מוציאים אדם מהכיתה. אם זו בת, משאירים אותה בחוץ. אם זה בן, מכניסים אחת במקומו. לאחר מכן מוציאים שוב אדם מהכיתה. נחשב את ההסתברויות השו

1. **Nyatakan masalah:** Kita diberi satu set kad bernombor: $\{2, 3, 4, 7, 10, 11, 12, 15, 21, 24\}$. Kita perlu cari kebarangkalian bagi dua peristiwa: (a) nombor perdana dan (b)

1. The problem states that Jamie has a probability of $\frac{1}{3}$ to hit the target on any single attempt. 2. We are told the probability that Jamie hits the target for the first

1. **Problem Statement:** We are given that Jamie has a probability of $\frac{1}{3}$ to hit a target on any attempt. 2. The probability that he hits the target for the first time o

1. **Problem Statement:** Jamie has a probability of hitting a target as $\frac{1}{3}$. We want to find the attempt number $n$ when he hits the target for the first time, given the

1. The problem states that Jamie has a probability of $\frac{1}{3}$ to hit a target on any single attempt. 2. We are told the probability that Jamie hits the target for the first t

1. **State the problem:** We want to find the probability that both chocolates picked are toffee, given the tree diagram with probabilities. 2. **Understand the tree diagram:**

1. **State the problem:** We want to find the probability that both chocolates picked are toffee, given the tree diagram probabilities. 2. **Understand the tree diagram:**

1. **State the problem:** We have a class of 31 students. Some revised and some did not. Among those who revised, 11 passed and 7 did not pass. Among those who did not revise, 5 pa

1. **State the problem:** We want to find the fraction of days when it actually hailed and Leon's prediction was correct. 2. **Identify relevant data:** From the frequency tree:

1. **Problem statement:** Jamie has a 1 in 3 chance to hit the target each time he tries. We know the chance he hits the target for the first time on his $n^{th}$ try is $\frac{64}

1. **Problem statement:** We are given that Jamie's probability of hitting the target on any attempt is $\frac{1}{3}$. The probability that he hits the target for the first time on

1. The problem is to understand the meaning of "favourable" and "unfavourable" cases in probability and statistics. 2. In probability, a "favourable case" refers to an outcome or e

1. **Stating the problem:** We are asked to determine the type of events when considering the events of getting prime numbers and odd numbers. 2. **Understanding the events:**

1. **Problem Statement:** We have a continuous random variable $X$ representing the total number of hours (in units of 100 hours) a family runs a vacuum cleaner in a year. The prob