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Stat400Lec2(Ch1.4,1.6)_ans

# Stat400Lec2(Ch1.4,1.6)_ans - Review Chapter 1.2 The...

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Review: Chapter 1.2 The probability that a randomly selected student at UIUC owns a bicycle is 0.55, the probability that a student owns a car is 0.30, and the probability that a student owns both is 0.10. C C' B B' (a) What is the probability that a student selected at random owns either a car or a bicycle, or both? P( B C ) = P( B ) + P ( C ) P( B C ) = 0.55 + 0.30 0.10 = 0.75. OR P( B C ) = P( B C ) + P( B ' C ) + P( B C' ) = 0.10 + 0.20 + 0.45 = 0.75. OR P( B C ) = 1 P( B ' C' ) = 1 0.25 = 0.75. (b)What is the probability that a student selected at random has neither a car nor a bicycle? P( B ' C' ) = 0.25.

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Chapter 1.4 Conditional Probability What is conditional probability? Multiplication Law of Probability How to calculate probabilities using the probability rules?
A Game: Monty Hall problem The Monty Hall problem is a probability puzzle based on the American television game show Let’s make a deal. Suppose you're on this show. You're given the choice of three doors. You know previously that, behind one door, there is a car; behind the other two doors, there is a goat behind each of the two doors. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? http://math.ucsd.edu/~crypto/Monty/monty.html

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Conditional Probability Conditional probabilities reflect how the probability of an event can change if we know that some other event has occurred or is true. The probability that a random student will get an “A” on the midterm (event B) is different if we choose from students who studied (event A) or students who didn’t (event C). The conditional probability of event A given event B is: (provided that P(B) ≠ 0) ) ( ) ( ) | ( B P B A P B A P
Car /Bicycle Example -- Revisit C C' B 0.10 0.45 0.55 B' 0.20 0.25 0.45 0.30 0.70 1.00 The probability that a randomly selected student at UIUC owns a bicycle is 0.55, the probability that a student owns a car is 0.30,

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