Complexity Explorer Santa Few Institute

Introduction to Information Theory

Lead instructor: Seth Lloyd

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When you are finished, clicking the "Score" button at the bottom of the test will show you the correct responses.

Question 1: What is the number of possible sequences of 10 coin tosses in which there are 7 heads and 3 tails?
Answer 1: A. 21
Answer 2: B. 120
Answer 3: C. 441
Answer 4: D. 1024
Question 2: Suppose you flip a biased coin, which lands on heads with probability 0.6. How much information is generated on average by each flip of the coin?
Answer 1: A. 0.17 bits
Answer 2: B. .33 bits
Answer 3: C. 0.97 bits
Answer 4: D. 2.36 bits
Answer 5: E. 2.58 bits
Question 3: Suppose you throw a six-sided die, and this die is fair (i.e., lands with the same probability on each side). How much information is generated on average by each throw of the die?
Answer 1: A. 0.17 bits
Answer 2: B. .33 bits
Answer 3: C. 0.97 bits
Answer 4: D. 2.36 bits
Answer 5: E. 2.58 bits
Question 4: We throw a six-sided die. However, this die is biased, so that it has probability 0.4 of landing on side 1, while the remaining probability is uniformly split between the remaining 5 sides. How much information is generated on average by each throw of this die?
Answer 1: A. 0.17 bits
Answer 2: B. 0.33 bits
Answer 3: C. 0.97 bits
Answer 4: D. 2.36 bits
Answer 5: E. 2.58 bits