A teacher announces a pop quiz for which the student
A teacher announces a pop quiz for which the student is completely unprepared. The quiz consists of 100 true-false questions. The student has no choice but to guess the answer randomly for all 100 questions.
a. Simulate taking this quiz by random guessing. Number a sheet of paper 1 to 100 to represent the 100 questions. Write a T (true) or F (false) for each question, by predicting what you think would happen if you repeatedly flipped a coin and let a tail represent a T guess and a head represent an F guess. (Don’t actually flip a coin, but merely write down what you think a random series of guesses would look like.)
b. How many questions would you expect to answer correctly simply by guessing?
c. The table shows the 100 correct answers. The answers should be read across rows. How many questions did you answer correctly?
d. The above answers were actually randomly generated by the Simulating the Probability of Head with a Fair Coin applet on the text CD. What percentages were true and what percentage would you expect? Why are they not necessarily identical?
e. Are there groups of answers within the sequence of 100 answers that appear nonrandom? For instance, what is the longest run of Ts or Fs? By comparison, which is the longest run of Ts or Fs within your sequence of 100 answers? (There is a tendency in guessing what randomness looks like to identify too few long runs in which the same outcome occurs several times in a row.)
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