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Home Question Bank Math Probability Archive 2025 January 12

Probability Questions from Jan 12,2025

Browse the Probability Q&A Archive for Jan 12,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Ivanna has a deck of 10 cards numbered 1 through 10 . She is playing a game of chance. This game is this: Ivanna chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses \( \$ 5.50 \) if an odd numbered card is drawn. \[ \begin{array}{l}\text { (a) Find the expected value of playing the game. } \\ \text { (b) What can Ivanna expect in the long run, after playing the game many times? } \\ \text { (She replaces the card in the deck each time.) } \\ \text { Ivanna can expect to gain money. } \\ \text { She can expect to win } \square \text { dollars per draw. } \\ \text { O Ivanna can expect to lose money. } \\ \text { She can expect to lose } \square \text { dollars per draw. } \\ \text { O Ivanna can expect to break even (neither gain nor lose money). }\end{array} \] Answer the questions below. \[ \begin{array}{l}\text { (a) From the } 12 \text { albums released by a musician, the recording company wishes to release } 10 \text { in a } \\ \text { boxed set. How many different boxed sets are possible? } \\ \text { (b) A company that makes crayons is trying to decide which } 3 \text { colors to include in a promotional } \\ \text { mini-box of } 3 \text { crayons. The company can choose the } 3 \text { mini-box colors from its collection of } 75 \\ \text { colors. How many mini-boxes are possible? } \\ \square\end{array} \] A bag contains eight balls labeled 1 through 8 . One ball will be randomly picked. What is the probability of picking an even number? Write your answer as a fraction. If you draw a card from a deck and do not replace it, what type of events does this represent when drawing a second card? 31. En un bulto de café hay granos con diferentes niveles de cafeína, bajo, medio y alto. Si al extraer un grano de café del bulto la probabilidad de que este sea un grano con nivel bajo de cafeína es 0,27 , ¿cuál es la probabilidad de que al extraer un grano este tenga un nivel medio o algo de cafeína? Alto Exercice 2. Lors du comptage des globules blancs dans une prise de sang, on distingue en général 5 catégories de globules blancs : polynucléaires neutrophiles, polynucléaires éosinophiles, polynucléaires basophiles, lymphocytes, monocytes. On considère que la probabilité d'observer dans le sang un polynucléaire neutrophile est de 0,6 . Sur 5 globules blancs, quelle est ta probabilite d'obtenir au moins 2 polynucléaires neutrophiles (donc d'obtenir \( 2,3,4 \) ou 5 neutrophiles parmi les 5 globules blancs)? JUNE 2022 2. If \( A \) and \( B \) are two events such that \( P(A)=0.54 \), \( P(B)=0.69 \) and \( P(A \cap B)=0.35 \) then find a) \( P(A \) or \( B) \) b) \( P \) (not \( A \) and not \( B) \) If \( A \) and \( B \) are two events such that \( P(A)=0.42 \), \( P(B)=0.48 \) and \( P(A \) and \( B)=0.16 \) then find: a) \( P(A \) or \( B) \) b) \( P\left(A^{\prime} \cap B^{\prime}\right) \) related scenarios involving permutations. 2. How many different ways can the 8 participants be arranged in a performance lineup? 3. If only 3 out of the 8 participants are chosen for a special act, and the order of performance matters, how many arrangements are possible? 4. If two participants insist on performing one after the other, how many valid arrangements can be made for the 8 participants? 5. If three participants are indistinguishable (e.g., they form a group act), how many unique arrangements can be made for all 8 participants? 6. Suppose 2 out of the 8 participants are unavailable for the show. How many ways can the remaining 6 participants be arranged in the lineup? For numbers \( 7-11 \), refer to the scenario below. Show your solutions on a sheet of paper. Refer to the criferia given in assessing your answer. A group of 6 friends decides to sit around a round table for dinner. Since the table is circular, the arrangement of the friends depends only on their relative positions (e.g., sitting clockwise or counterclockwise). They want to explore different seating arrangements and scenarios involving specific constraints, such as certain friends sitting next to each other or in a specific For numbers \( 2-6 \), refer to the scenario below. Show your solutions on a sheer of paper. Refer to the criteria given in assessing your answer. A school is organizing a talent show. There are 8 participants, and the order in which they perform matters. The organizers want to determine the number of ways to arrange the performers, select a specific group for a special act, and explore other related scenarios involving permutations. How many different ways can the 8 participants be arranged in a performance lineup? If only 3 out of the 8 participants are chosen for a special act, and the order of performance matters, how many arrangements are possible? If two participants insist on performing one after the other, how many valid arrangements can be made for the 8 participants? If three participants are indistinguishable (e.g., they form a group act). how many unique arrangements can be made for all 8 participants? Suppose 2 out of the 8 participants are unavailable for the show. How many ways can the remaining 6 participants be arranged in the lineup? For numbers 7 -LI. refer to the scenario below. Show your solutions on a sheet of paper. Refer to the criteria given in
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