🎲 probability

1. **State the problem:** We have two bags:

1. **Problem statement:** Find the probability that the third ball drawn is red when balls are drawn without replacement from a bag containing 6 red and 9 green balls.

1. **Problem statement:** We have 60 students: 35 study French, 45 study Spanish, and 27 study both.

1. Énoncé du problème 70 : Soient A et B deux événements incompatibles de probabilité non nulle. Démontrer que A et B ne sont pas indépendants. 2. Rappel des définitions :

1. **Stating the problem:** We want to calculate the probability of exactly 6 successes in 25 trials with success probability $p=0.26$ using the binomial formula. 2. **Formula used

1. **Problem:** An urn contains 10 balls: four '4's, three '3's, two '2's, and one '1'. Two balls are drawn without replacement. Find the probability that the first ball is '1' giv

1. **State the problem:** We have a total of 19 items in the universal set $\xi$. Sets $M$ and $N$ are subsets of $\xi$ with the following counts: - $8$ items in $M$ only

1. **Énoncé du problème :** Une maternité a enregistré 1 750 accouchements en 2019. On sait que 8 % des femmes ont accouché prématurément, 6 % ont fumé régulièrement durant les tro

1. **Problem:** A four-sided die labelled 1, 2, 3, and 4 is rolled and a spinner labelled 3, 6, and 9 is spun. Create a table to show the sample space. 2. **Sample Space Table:** T

1. **Problem Statement:** We are given the probability density function (pdf) of the standard normal distribution:

1. **Stating the problem:** We want to find the probability that two customers selected at random both require a takeout box.

1. **Stating the problem:** Given probabilities:

1. **State the problem:** We have a critical airline component with a failure probability of $0.0058$. The system uses triple modular redundancy, meaning there are three independen

1. **State the problem:** We want to find the probability of choosing three letters from the word FACETIOUS such that the letters are A, E, and I in any order. 2. **Identify total

1. **Problem statement:** A coin is flipped twice and then a four-sided die (with numbers 1, 2, 3, and 4) is rolled. The coin and the die are both fair. (i) Complete the sample spa

1. **State the problem:** We have a spinner spun 100 times. The frequency of red is 35, and the ratio of black to red frequencies is 2:7. We need to find the estimated probability

1. The problem asks to convert the scientific notation $1.61 \times 10^{-7}$ into an ordinary decimal number. 2. Scientific notation $a \times 10^{n}$ means move the decimal point

1. **State the problem:** We have a probability tree diagram involving two people, Jack and Charlie. Jack has a probability of qualifying as $\frac{3}{10}$ and not qualifying as $1

1. **Stating the problem:** We want to find the probability that Sean does **not** win either the chess game or the pool game.

1. **State the problem:** We have a probability distribution with amounts won and their probabilities:

1. The problem is to understand a probability question, but since no specific probability problem is given, I will explain the basics of probability. 2. Probability measures how li