3.21. La belote se joue avec un jeu de 32 cartes, chaque carte possédant une valeur ( \( 7,8,9,10 \), Valet, Dame, Roi, As) ainsi qu'une couleur (pique, trèfle, coeur, carreau). 1. Au départ, chaque joueur possède une main de cinq cartes. (a) Combien de mains différentes existe-t-1? (b) Combien de mains ne comportant que des piques existe-t-il? (c) Combien de mains ayant exactement quatre carreaux existe-t-1? 2. A la fin de la deuxième donne, chaque joueur possède alors huit cartes dans sa main. (a) Combien de mains de huit cartes existe-t-il? (b) Combien de mains de huit cartes ayant exactement cinq cours existe-t-il? (c) Même question avec six, sept et huit cours. (d) En déduire le nombre de mains de huit cartes avec au moins cinq cceurs.

A three-digit number is to be formed from the digits 1,6 and 8 . What is the probability that the number will:

A six-sided die is rolled. Let A be the event "getting an odd prime number". (1) Write down the set \( \mathrm{A}, \mathrm{n}(\mathrm{A}) \) and \( \mathrm{P}(\mathrm{A}) \). (2) Draw a Venn diagram showing the actual outcomes. (3) Draw a Venn diagram showing the number of outcomes. (4) Draw a Venn diagram showing the probabilities.

Someone hands you a box of 13 chocolate-covered candies, telling you that 6 are vanilla creams and the rest are peanut butter. You pick candies at random and discover the first 3 you eat are all vanilla. Consider a result to be surprising if there is less than a \( 5 \% \) chance of observing it given your expectations. Complete parts a through c below. a) If there really were 6 vanilla and 7 peanut butter candies in the box, what is the probability that you would have picked 3 vanillas in a row? (Round to three decimal places as needed.)

The probability that it will be suminy tomorrow is \( \frac{2}{9} \), If it is sunny, the probability tha Siya plays rugby is \( \frac{8}{15} \). If it is not sumy, the probability that Stya plays rugby is \( \frac{4}{15} \) 9.2.1 Represent the above information on the tree diagram and indicate all the possible outcomes.

The probability that it will be sunny tomorrow is \( \frac{2}{9} \). If it is sunny, the probability that Siya plays rugby is \( \frac{8}{15} \). If it is not sunny, the probability that Siya plays rugby is \( \frac{4}{15} \) 9.2.1 Represent the above information on the tree diagram and indicate all the possible outcomes.