problemset05 - STAT/MA 416 Problem Set 5 Name 1 Waking up...

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STAT/MA 416 August 31, 2011 Problem Set 5 Name: 1. Waking up at random. On each weekday, a student wakes up before 8 AM with probability . 65, or after 8 AM with probability . 35. On each weekend, a student wakes up before 8 AM with probability . 22, or after 8 AM with probability . 78. Suppose that a student wakes up and can’t remember which day it is! (a.) If the student sees that it is before 8 AM, what is the probability it is a weekday? (b.) If the student sees that it is after 8 AM, what is the probability it is a weekday? 1
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2. Socks. A matching pair of blue socks, a matching pair of red socks, and one lone white right-footed sock are in a drawer. Suppose that a person blindly pulls a sock out of the drawer and it is not red (i.e., it is either the white sock or one of the blue socks). He discards this sock, so four socks remain. Now he reaches into the drawer again and chooses a sock at random from the four socks that remain. What is the probability that this sock is blue? 2
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3. Pair of dice. Roll a blue die and a red die. Given that the blue die has an odd value,
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