Exercice 1 Soit \( (X, Y) \) un couple aléatoire à valeurs dans \( \mathbb{R}^{2} \) admettant la densité 1. Déterminer \( C \)

Question 12 If \( P(A)=0.15, P(B)=0.2 \), and \( A \) and \( B \) are independent, Find \( P(A \) and \( B) \). Add your answer Integer, decimal, or E notation allowed

Question 19 In a survey, 46\% of Americans say they suffer great stress at least once a week. If three people are selected at random, what is the probability that all three will say that they suffer great stress at least once a week? Add your answer Integer, decimal, or E notation allowed

If \( P(A)=0.25, P(B)=0.6 \), and \( P(A \) and \( B)=0.2 \), are \( A \) and \( B \) independent? A) No (B) Yes

Two newspapers \( A \) and \( B \) are published in a city. It is known that \( 25 \% \) of the city populations reads \( A \) and \( 20 \% \) reads \( B \) while \( 8 \% \) reads both \( A \) and \( B \). Further, \( 30 \% \) of those who read \( A \) but not \( B \) look into advertisements and \( 40 \% \) of those who read \( B \) but not \( A \) also look into advertisements, while \( 50 \% \) of those who read both \( A \) and \( B \) look into advertisements. Then the percentage of the population who look into advertisement is [JEE (Main) 2019] \( \begin{array}{ll}\text { (a) } 12.8 & \text { (b) } 13.5 \\ \text { (c) } 13.9 & \text { (d) } 13\end{array} \)

Question 9 Suppose that \( E \) and \( F \) are two events and that \( P(E \) and \( F)=0.28, P(A)=0.29 \) and \( P(E)=0.43 \). What is \( P(F \mid E) \) ? Add your answer Integer, decimal, or E notation allowed