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Home Question Bank Math Probability Archive 2024 November 02

Probability Questions from Nov 02,2024

Browse the Probability Q&A Archive for Nov 02,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Evaluate \( { }_{9} \mathrm{P}_{3} \) and \( { }_{9} C_{4} \). \( { }_{9} P_{3}=\square \) \( { }_{9} C_{4}=\square \) Suppose we want to choose 5 letters, without replacement, from 15 distinct letters. (a) How many ways can this be done, if the order of the choices matters? \( \square \) (b) How many ways can this be done, if the order of the choices does not matter? \( \square \) A spinner has 20 equally sized sections, 4 of which are green and 16 of which are blue. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads? Do not round your answer. A spinner has 20 equally sized sections, 4 of which are green and 16 of which are blue. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads? Do not round your answer. Suppose that \( A \) and \( B \) are independent events such that \( P(A)=0.10 \) and \( P(\bar{B})=0.40 \). Find \( P(A \cap B) \) and \( P(A \cup B) \). \( \begin{array}{l}\text { (a) } P(A \cap B)=\square \\ \text { (b) } P(A \cup B)=\square\end{array} \) Let \( M \) and \( N \) be two events such that \( P(M)=0.22 \) and \( P(N)=0.24 \). Do not round your responses. (a) Determine \( P(M \cup N) \), given that \( M \) and \( N \) are independent. (b) Determine \( P(M \cup N) \), given that \( M \) and \( N \) are mutually exclusive. \( \square \) What is a discrete probability distribution? What are the two conditions that determine a probability distribution? \( \begin{array}{l}\text { What is a discrete probability distribution? Choose the } \\ \text { correct answer below. }\end{array} \) \( \begin{array}{l}\text { B. A discrete probability distribution lists each } \\ \text { possible value a random variable can assume. } \\ \text { possible value a random variable can assume, } \\ \text { together with its probability. } \\ \text { probabilities. }\end{array} \) D. None of the above Example 2: (a) Find the expectation of the number on a die when thrown. (b) Two unbiased dice are thrown. Find the expected values of the sum of numbers of points on them. find the expectation and varience of sei number of heads in three tosses of a coin. Un grupo de estudiantes está conformado por ca- torce niños y doce niñas. Considera los sucesos: A: "seleccionar dos niños". B: "seleccionar dos niñas". a. Halla el suceso \( A \cup B \) y su probabilidad. b. Calcula \( P(\bar{A}) \).
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