Final answer:
If you tell me the number of the winning tickets in a lottery where each digit is randomly chosen from the set {0, 1, ..., 9}, you have given me 16 bits of information.
Step-by-step explanation:
The winning number in the lottery is made up of four pairs of digits, such as 84-97-00-91. Each digit is randomly selected from the set {0, 1, ..., 9}. If you provide the number of the winning ticket, you have given me 16 bits of information.
To calculate the information content, we need to find the number of possible outcomes. In this case, there are 10 choices for each digit, and we have 4 pairs of digits, so the total number of outcomes is 10^8 (since 10 * 10 * 10 * 10 = 10^4). Taking the base-2 logarithm of 10^8 gives us 26.57 bits. However, each pair of digits is independent, so we divide by 2 to get 13.29 bits for each pair. Since we have 4 pairs, the total information content is 4 * 13.29 = 53.16 bits. Rounded to the nearest whole number, we have 53 bits, but since you have provided the number of the winning ticket, we only need to convey the remaining information which is 53 - 37 = 16 bits.