(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?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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1 b)
Transcribed Image Text:(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?
(d) Suppose your roommate guessed 9 of the 20 zodiac signs correctly. If they were just
guessing randomly, what is the probability that they would do at least as well as 9
correct?
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