fall 2006 STAT 230 Quiz2Solutions

fall 2006 STAT 230 Quiz2Solutions - STAT 230 Quiz #2 Oct...

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Unformatted text preview: STAT 230 Quiz #2 Oct 12, 2006 3:40 4:10 pm Name: S I.D: UWUserid: Mark /20 Circle your instructor and time slot: 1. Metzler(1:30) 2. Drekic(11:30) 3. Springer(10:30) 4. Drekic(12:30) 5. Ramirez(8:30) 1. I have two coins. Coin A shows heads 50% of the time, Coin B shows heads 80% of the time. One of the coins is chosen at random, and that coin is flipped 5 times (each coin is equally likely to be chosen). [4] (a) What is the probability I get 5 consecutive heads? P (5H) = P (5H | A chosen) P (A chosen) + P (5H | B chosen) P (B chosen) = ( . 5) 5 ( . 5) + ( . 8) 5 ( . 5) = . 179465 [4] (b) Given that I got 5 consecutive heads, what is the probability that Coin B was chosen? P (B chosen | 5H) = P (5H | B chosen) P (B chosen) P (5H) = ( . 8) 5 ( . 5) . 179465 = . 9129 [3] (c) Are the events Coin B chosen and 5 consecutive heads independent? Justify your answer. These events are not independent. There are several acceptable ways to show this P (5H B chosen) = ( . 5)( . 8)...
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fall 2006 STAT 230 Quiz2Solutions - STAT 230 Quiz #2 Oct...

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