Unformatted text preview: ST 561: Preparation for Quiz 1 (not to hand in) 1. (The Infamous Monty Hall problem). There are 3 doors. Behind one door is a car; behind
the other two doors there are goats. You choose one door. Monty Hall opens another door and a goat appears — then he asks you if you want to switch and choose the remaining door. Should you
switch? ' 2. 'vao dice are rolled. X = # of spots on die 1; Y = #z of spots on die 2. Let Z 2 X + Y.
Find P(X > 1|Z :4) and P(Z 2 4|X > 1). 3. In a lot of 50 light bulbs, there are two bad bulbs. An inspector examines ﬁve bulbs, which
are selected at random and without replacement. a. Find the probability of at least one defective bulb among the ﬁve. b. How many bulbs should be examined so that the probability of ﬁnding at least one bad bulb
exceeds 1/2? 4. If f(.'1:) : c(2/3)‘” for 53 z 1, 2,2, ...., ﬁnd the value of c that makes f(a:) a probability mass
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- Fall '08