🎲 probability

1. **Problem Statement:** We are given probabilities of weather conditions and the probability of a bus being late under each condition. We need to:

1. **Problem Statement:** We want to verify the sum of probabilities for all possible outcomes when drawing two fruits sequentially without replacement from a basket containing 7 l

1. **State the problem:** We have 1000 tickets sold in a raffle, and one winning ticket is picked at random. Jack has one ticket. We want to find the probability that Jack's ticket

1. **State the problem:** We want to find the probability that Xavier and Yvonne solve the problem, but Zelda does not. 2. **Given probabilities:**

1. **Problem statement:** Given a binomial random variable $X$ with $E(X) = 6.5$ and $\text{Var}(X) = 3.25$, find: (1) $\Pr(X = 6)$

1. **Problem statement:** We want to estimate the number of runners in the London Marathon on 25th April 2010 whose birthday was on that exact day. 2. **Understanding the problem:*

1. **Problem Statement:** We have a test for cancer detection with the following data:

1. **Problem Statement:** Two dice are thrown simultaneously. We need to find the probability that the sum of the numbers on the dice is greater than 5 and less than 8. 2. **Total

1. The problem involves understanding conditional probabilities and categorizing individuals based on gender and whether they have a problem with an issue. 2. We define the events:

1. **Markov Chain Problem 1: Two Products A and B** Problem: Given initial proportions and switching probabilities, find:

1. **State the problem:** We want to find the probability that when a six-sided die is rolled six times, the number 1 appears exactly once. 2. **Identify the distribution:** This i

1. The term "all the probabilities" is broad, so let's clarify that probabilities are values between 0 and 1 that represent the likelihood of an event occurring. 2. The probability

1. The problem asks to calculate the total number of possible outcomes for 20 football matches, where each match can result in one of three outcomes: win, lose, or draw. 2. Since e

1. Let's define the probabilities for a single football match: win = $p_w$, lose = $p_l$, draw = $p_d$. 2. Since these are the only outcomes, they must satisfy $p_w + p_l + p_d = 1

1. Let's start by understanding what probability means. Probability measures how likely an event is to occur, and it ranges from 0 (impossible event) to 1 (certain event). 2. The b

1. The problem is to understand the values of $n=5$ and $p=0.55$ in a binomial distribution context. 2. Here, $n$ represents the number of trials, which is 5.

1. The problem asks for the probability that the sample contains more than three students who do not live in the dormitories. 2. Let $X$ be the random variable representing the num

1. **Énoncé du problème :** L'université propose trois filières A, B, C avec des effectifs liés : $|A|=2|B|$ et $|B|=3|C|$. On cherche les probabilités associées aux événements A,

1. **Nyatakan masalah:** Diberi kebarangkalian Linda (L) menyertai lawatan ialah $\frac{2}{5}$ dan Shukri (S) ialah $\frac{3}{8}$. Kita perlu lengkapkan gambarajah pokok dan hitung

1. **State the problem:** We have a bag with 5 red balls and 3 blue balls. We want to find the probability of picking a blue ball. 2. **Total number of balls:** The total number of

1. **State the problem:** We are given that the probability a robot fails during any 6-hour shift is $p=0.10$. We want to find the probability that the robot operates through at mo