🎲 probability

1. **State the problem:** We want to find the probability that the grinding mill does not break down at all in a month, given the average breakdown rate $\lambda = 5$ times per mon

1. **Problem statement:** We have 15 coupons numbered 1 to 15. We select 7 coupons with replacement. We want the probability that the largest number appearing among the selected co

1. **Problem statement:** Formulate the complementary events (Gegenereignisse) for the following events when randomly marking answers to five tasks. 2. **Recall:** The complementar

1. **Problem statement:** We are given that 7% of teachers are computer science teachers, and the rest are other teachers. Among the other teachers, 94% use MS-Office. Among the co

1. مسئله: یک کلاس شامل ۳ فارغ التحصیل و ۹ دانشجو است که به طور تصادفی به ۳ گروه ۴ نفری تقسیم می‌شوند. احتمال اینکه هر گروه شامل دقیقاً یک فارغ التحصیل باشد چقدر است؟ 2. فرمول‌ها و

1. The problem asks for the probability that the bus driver is playing Mitski. 2. Probability is calculated as the ratio of favorable outcomes to total possible outcomes: $$P(E) =

1. **Problem Statement:** The probability that a patient fails to recover from a heart transplant operation is 0.5% (or 0.005). Eight patients are selected at random for the operat

1. **State the problem:** We have a bag containing 29 balls numbered from 1 to 29. 2. **What is asked?** Find the probability of choosing a ball numbered 30.

1. The problem is to represent the approximation of binomial distributions to normal distributions for probabilities $p=0.5$ and $p=0.05$ with sample sizes $n=3, 25, 50$. 2. The bi

1. مسئله: در پرتاب دو تاس، اگر بدانیم جمع دو عدد کمتر از 6 است، احتمال اینکه هر دو عدد برابر باشند را بیابیم. 2. فرمول احتمال شرطی: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ که در آن:

1. **Stating the problem:** We have a Markov chain with transition matrix $$P = \begin{bmatrix}0.825 & 0.175 & 0.000 \\ 0.060 & 0.919 & 0.021 \\ 0.049 & 0.000 & 0.951 \end{bmatrix}

1. **Problem:** Eine Spielerin hat nach dem ersten Wurf die Augenzahlen $4-4-5-6-6$ und möchte mit den nächsten zwei Würfen die Große Straße $2-3-4-5-6$ erreichen. 2. **Formel und

1. **Énoncé du problème :** On considère un échantillon de 15 tomates prises au hasard dans un stock où 9 % des tomates ne sont pas commercialisables.

1. **State the problem:** We want to find the probability of winning a carnival game where winning means tossing a coin and getting Heads, and rolling a die and getting a 6. 2. **F

1. **State the problem:** Bill spins two spinners, Spinner A with numbers \(8, 4, 2, 1\) and Spinner B with numbers \(7, 9, 5, 3\). He wins a prize if the sum of the numbers from b

1. **Problem Statement:** Bill spins two spinners, Spinner A with numbers 8, 4, 2, 1 and Spinner B with numbers 7, 9, 5, 3. We need to complete the addition chart showing the sums

1. **State the problem:** Find the probability that a baseball player with a batting average of 0.28 hits exactly 4 times in 12 at-bats.

1. **Problem:** Find the theoretical probability that a number less than 3 is rolled on a cube numbered 1 through 6. 2. **Formula:** Probability $P(E) = \frac{\text{number of favor

1. **Problem:** Describe an outcome that is certain when selecting one card from a standard deck of 52 cards. 2. **Formula and rules:** The probability of a certain event is always

1. **Stating the problem:** We have three insurance options A, B, and C with probabilities $\frac{1}{4}$, $\frac{1}{3}$, and $\frac{5}{12}$ respectively.

1. **State the problem:** We have a group of people categorized by their mode of transportation: car only, bicycle only, both car and bicycle, and neither. 2. **Given data:**