Reference no: EM132351233
Exercise 1 (Dots and Dashes Extension). We are sending messages of 0s and 1s. Sometimes, transmission errors occur (a 0 accidentally gets changed to a 1, or a 1 accidentally gets changed to a 0). Suppose that 70% of numbers sent are 0s, and 70% of number received are 1s. 1s are always transmitted correctly.
1. What is the probability that a 0 is transmitted incorrectly?
2. Given that we receive a 0, what is the probability that a 0 was sent?
Exercise 2 (Shirts and Socks). Each day, I wear either a blue shirt, a green shirt, or a red shirt. I have the same number of shirts of each color, so each morning I pick one uniformly at random. I also wear either blue, green, or red socks. I like to match, so given that I wear a red shirt, there is a 70% chance I wear red socks, and equal chances that I wear blue socks or green socks. Similarly, if I wear a blue shirt, there is an 70% chance that I wear blue socks, and equal chances that I wear red socks or green socks. If I am wearing a green shirt, there is a 90% chance I am wearing green socks, with the other two colors being equally likely.
1. What are the chances that my shoes and socks match?
2. Given that I am wearing red socks, what is the probability that I am wearing a red shirt?
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