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Probability Questions from Jan 20,2025

Browse the Probability Q&A Archive for Jan 20,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Let the universal set, \( U \), be the set of students at Central High, \( A \) be the set of students taking algebra, and \( C \) be the set of students taking chemistry. If a student is selected at random, describe in words what is meant by each of the following probabilities. a. \( P(A \cup C) \) b. \( P(A \cap C) \) c. \( 1-P(C) \) When a particular type of thumbtack is dropped, it will land point up \( (\perp) \) or point down \( (K) \). This experiment was repeated 80 times with the following results: point up: 48 times; point down: 32 times. a. What is the experimental probability that a particular type of thumbtack will land point up? b. What is the experimental probability that a particular type of thumbtack will land point down? c. If the experiment was tried another 80 times would the same results occur? Why? d. Is it expected that nearly the same results occur on a second trial? Why? When a particular type of thumbtack is dropped, it will land point up \( (\perp) \) or point down ( \( < \) ). This experiment was repeated 100 times with the following results: point up: 50 times; point down: 50 times. a. What is the experimental probability that a particular type of thumbtack will land point up? b. What is the experimental probability that a particular type of thumbtack will land point down? c. If the experiment was tried another 100 times would the same results occur? Why? d. Is it expected that nearly the same results occur on a second trial? Why? When a particular type of thumbtack is dropped, it will land point up ( \( \perp \) ) or point down ( \( \langle \) ). This experiment was repeated 100 times with the following results: point up: 50 times; point down: 50 times. a. What is the experimental probability that a particular type of thumbtack will land point up? b. What is the experimental probability that a particular type of thumbtack will land point down? c. If the experiment was tried another 100 times would the same results occur? Why? d. Is it expected that nearly the same results occur on a second trial? Why? a. The experimental probability that a particular type of thumbtack will land point up is (Type an integer or a simplified fraction.) If \( A \) and \( B \) are mutually exclusive, and if \( P(A)=0.2 \) and \( P(B)=0.7 \), what is \( P(A \cup B) \) ? \( P(A \cup B)=\square \) 90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathematics majors. No person has a double major. If a single calculus student is chosen, find the following probabilites. Find the probability that the student is a man. P (man) \( =\frac{9}{17} \) (Type an integer or a simplified fraction.) Find the probability that the student is a mathematics major P (mathematics) \( =\frac{11}{34} \) (Type an integer or a simplified fraction.) Find the probability that the student is not a computer science major. P(not computer science) \( =\frac{23}{34} \) (Type an integer or a simplified fraction.) Find the probability that the student is a mathematics major or a computer science major. P(mathematics \( u \) computer science) \( =\square \) (Type an integer or a simplified fraction.) 90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathematics majors. No person has a double major. If a single calculus student is chosen, find the following probabilities. Find the probability that the student is a man. \( P \) (man) \( =\frac{9}{17} \) (Type an integer or a simplified fraction.) Find the probability that the student is a mathematics major. P(mathematics) \( =\frac{11}{34} \) (Type an integer or a simplified fraction.) Find the probability that the student is not a computer science major. P(not computer science) \( =\square \) (Type an integer or a simplified fraction.) What is the definition of a compound event in probability? 90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathema majors. No person has a double major. If a single calculus student is chosen, find the following probabilities. b. The card is an odd number and the card is a prime number. The events
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