1. (10 pts.) Suppose you have a language with only 3 letters: A, B, and C, which occur with frequencies 0.7, 0.2, and 0.1, respe
ctively. The following ciphertext was encrypted by the Vigen`ere method: BABABCBCAC. Assume that the key length is either 1, 2, or 3. Find the most likely key length and determine the most likely key using the method from class. Solution: We compare BABABCBCAC with its shifts by 1, 2, and 3, looking for overlaps. There are no overlaps for a shift of 1 or 3, but there are 6 overlaps for a shift of 2. Thus we expect the key length to be 2. Looking at every other letter, we see BBBBA and AACCC for the letters in even and odd positions, respectively. Due to the overwhelming frequency of the letter A in the language, we can reasonably assume that B decrypts to to A in the first sequence and C decrypts to A in the second. This gives us the key BC.
1 answer:
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Answer:
20 people only buy dvds.
Step-by-step explanation:
There are two groups in this problem. One group of people that buys dvds and one that buys blu rays. The total amount of people who buy blu rays is 300, but there's an intersection between the groups and the size of this is 280 people who actually buy both. In order to find out how many people only buy DVDs we first need to figure out how many only buy blu-rays. That is:
people who only buy blu rays = people who buy blu rays - people who buys blu rays and dvds
people who only buy blu rays = 300 - 280 = 20
We can now calculate the amount of people who only buy dvds and that is:
people who only buy dvds =total amount of people - ( people who only buy blu rays + people who buy both)
people who only buy dvds = 320 - (20 + 280) = 320 - 300 = 20 people
