PROBLEM Simon must answer two security questions in order to reset his forgotten password to his AOL account from 1996. The probability he remembers the answer to the first security question is .6 . The probability that he fails to remember the answer to the second question is .6. What is the probability that Simon successfully answers both questions correctly?

[Ch-Mo-Ra-Co] On tire successivement et avec remise \( n \) cartes ( \( n \in \mathbb{N}^{*} \) ) dans un jeu de 32 cartes et on note X la variable aléatoire qui compte le nombre de «Roi de cœur» tirés. 1) Quelle est la loi de probabilité de la variable aléatoire \( X \) ? Justifier. 2) Compléter les lignes 6,7 et 8 de la fonction Python simulroidecoeur ( \( n \) ) afin qu'elle simule la variable aléatoire \( X \). 3) Aider Léo à répondre à la question suivante: «Combien doit-on effectuer de tirages pour que la probabilité d'avoir au moins un roi de cœur soit supérieure ou égale à 0,95 ? ». Expliquer.

В урне имеется 4 шара, они пронумерованы числами: \( 1,2,3 \) и 4. Берём наугад один шар. Найдите вероятность того, что изображённое на нём число не будет 1. \( \begin{array}{llll}\text { 1) } \frac{1}{4} ; & \text { 2) } \frac{1}{2} ; & \text { 3) } \frac{1}{3} ; & \text { 4) } \frac{3}{4}\end{array} \)

5. Se tienen los 4 ases de una baraja y se quieren tomar al azar dos cartas. ¿Cuántas y cuáles son las combinaciones que pueden resultar?

В эксперименте предыдущей задачи найдите вероятность того, что сумма выпавших чисел равна 7. \( \begin{array}{llll}\text { 1) } \frac{1}{6} ; & \text { 2) } \frac{1}{12} ; & \text { 3) } \frac{1}{8} ; & \text { 4) } \frac{1}{10}\end{array} \)

10. The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. 7 were health care articles. If he liked all the articles equally, and randomly selected 5 articles to go on the front cover, how many ways can he choose which ones? 11. Anna got a summer job at a movie theater cleaning the aisles after each film. This Sunday, 7 movies are scheduled to show. If Anita is randomly assigned to clean up after 4 movies, how many ways can Anna's theaters be assigned? 12. Finn performs 10 exercises over the span of a week. 5 of his exercises involve biking. If he randomly chose 6 exercises to do on Monday, what is the probability that exactly 4 of the chosen exercises involve biking?