Let the amount of information obtained on being told that an event of probability p has occurred be −log₂ p bits. Which of the following is the amount of information obtained on being told that an event of probability 1/8 has occurred?

Answer: C. 3 bits

The amount of information is −log₂(1/8) = log₂ 8 = 3 bits. Since 1/8 = 1/2³, it is the same amount of information as being told the answer to a "one of two" question of probability 1/2 three times over. The less likely an event, the more information we receive on being told that it has occurred.

• A. 0.125 is the probability 1/8 itself. The amount of information is not the probability but −log₂ p.
• B. 0.375 is −(1/8) × log₂(1/8) = 3/8, the term this event contributes when calculating the entropy. It is not the amount of information itself.
• C. Correct. −log₂(1/8) = 3 bits.