(1) One of your roommates claims to have psychic powers. You are skeptical and design the following experiments to test their abilities: • You flip a coin, secretly write the result on a slip of paper, and ask your friend to identify the result (Head of Tail). You repeat this 20 times and record the total number X1 of times your roommate guessed correctly. • You randomly pick a sign of the zodiac (there are twelve), secretly write it on a slip of paper, and ask your friend to identify the sign. You repeat this 20 times and record the total number X2 of times your roommate guessed correctly. (a) If your friend is just guessing randomly, explain why X1 and X2 are Binomial random variables. What is the expected number of correct guesses for the coin flips? What is the expected number of correct guesses for the zodiac signs? (b) Calculate (without using a table) the probabilities P(X1 > 0) and P(X2 > 0). Show all work. (c) Suppose your roommate called 14 of the 20 coin flips correctly. If they were just guessing randomly, what is the probability that they would do at least as well as 14 correct?

(1) One of your roommates claims to have psychic powers. You are skeptical and design the following experiments to test their abilities: • You flip a coin, secretly write the result on a slip of paper, and ask your friend to identify the result (Head of Tail). You repeat this 20 times and record the total number X1 of times your roommate guessed correctly. • You randomly pick a sign of the zodiac (there are twelve), secretly write it on a slip of paper, and ask your friend to identify the sign. You repeat this 20 times and record the total number X2 of times your roommate guessed correctly. (a) If your friend is just guessing randomly, explain why X1 and X2 are Binomial random variables. What is the expected number of correct guesses for the coin flips? What is the expected number of correct guesses for the zodiac signs? (b) Calculate (without using a table) the probabilities P(X1 > 0) and P(X2 > 0). Show all work. (c) Suppose your roommate called 14 of the 20 coin flips correctly. If they were just guessing randomly, what is the probability that they would do at least as well as 14 correct?

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section: Chapter Questions

Problem 2RP: A Bitter Dispute With the publication of Ars Magna, a dispute intensified between Jerome Cardan and...

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