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Home Question Bank Math Probability Archive 2025 January 13

Probability Questions from Jan 13,2025

Browse the Probability Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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13 Un sac contient 5 boules blanches, 4 boules vertes et 3 boules rouges. 1. Détermine le nombre de manières de tirer en même temps 3 boules de même couleur. 2. Détermine le nombre de manières de tirer en même temps 3 boules de couleurs différentes deux à deux. 3. Détermine le nombre de manières de tirer en même temps 3 boules de couleurs différentes. tivity 2 a tick (/) if the events can happen at the same time and (X) if they can ppen at the same time on the box. 1) \( \mathrm{A}= \) tossing a coin and getting a head \( \mathrm{B}= \) tossing a coin and getting a tail 2) \( \mathrm{A}= \) rolling a die and getting a factor of 6 \( \mathrm{~B}= \) rolling a die and getting a prime number 3) \( \mathrm{A}= \) a heart is drawn from a standard deck of cards \( \mathrm{B}= \) a face card is drawn from a standard deck of cards 4) \( \mathrm{A}= \) an ' 8 ' is drawn from a standard deck of cards \( \mathrm{B}= \) a king is drawn from a standard deck of cards 5) \( \mathrm{A}= \) a multiple of 3 turning up in rolling a die once \( \mathrm{B}= \) a factor of 4 turning up in rolling a die once Sharon wants to sit in the back seat of the bus on the trip to the zoo. The back seat is the full width of the bus and seats five students. If Sharon selects her place on the seat at random, what is the probability that she will sit at either end by a 7. How many unique arrangements can be made with the letters in the word PERMUTATION? 15. While at the dollar store, Peter finds 19 items at \( \$ 1 \) each that he wants, but he only has \( \$ 3 \). The number of ways he could select which items to buy is \( \begin{array}{ll}\text { A. }{ }_{19} C_{0}+{ }_{19} C_{1}+{ }_{19} C_{2}+{ }_{19} C_{3} & \text { C. }\left({ }_{19} P_{0}\right)\left({ }_{19} P_{1}\right)\left({ }_{19} P_{2}\right)\left({ }_{19} P_{3}\right) \\ \text { B. }\left({ }_{19} C_{0}\right)\left({ }_{19} C_{1}\right)\left({ }_{19} C_{2}\right)\left({ }_{19} C_{3}\right) & \text { D. }{ }_{19} P_{0}+{ }_{19} P_{1}+{ }_{19} P_{2}+{ }_{19} P_{3}\end{array} \) - 5. For a mock United Nations, 6 boys and 7 girls are to be chosen. If there are 12 boys and 9 girls to \choose from, how many groups are possible? \( \begin{array}{ll}\text { A. } 846720 & \text { C. } 960 \\ \text { B. } 33264 & \text { D. } 120708403200\end{array} \) What is the definition of a compound event in probability? Exercice 51 : Une urne \( U_{1} \) contient 3 boules blanches et 4 noires et un urne \( U_{2} \) contient whes en 3 noires. On effectue \( n \) tirages \( \left(n \in \mathbb{N}^{*}\right) \) dans les conditions sivantes : - tous les tirages se font avec remise; - on effectue un premier tirage dans \( U_{1} \); - si un tirage donne une boule blanche, le tirage suivant se fait dans \( U_{1} \), son il se fait dans On note \( p_{n} \) la probabilité d'obtenir une boule blanche au \( n \)-ième tirage. 1. Déterminer \( p_{n+1} \) en fonction de \( p_{n} \). \( 15 A \) et \( B \) sont deux événements et \( P \) une probabilité . On donne \( P(A)=0,3, P(B)=0,5, P(A \cup B)=0,65 \) \( 1^{\circ} \) Calculer \( P(A / B) \). \( 2^{\circ} A \) et \( B \) sont-ils indépendants ? En déduire \( P(B / A) \). 17 On lance un dé parfait. Quelle est la probabilité d'obtenir le chiffre 6 sachant: \( 1^{\circ} \) que l'on a obtenu un résultat pair? \( \mathbf{2}^{\circ} \) que l'on a obtenu un résultat multiple de 3 ?
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