EE 131A
Problem Set #3
Probabilities
October 21, 2005
Instructor: Vwani Roychowdhury
Due: October 28, 2005
1. The amount of time cars are parked in a parking lot follows an exponential probability
law with average time of 1 hour. The charge for the parking is 1 dollar for each half
hour or less. Find the probability that a car pays k dollars.
2. Suppose we have 3 cards identical in form except that both sides of the ﬁrst card are
colored red, both sides of the second card are colored black, and one side of the third
card is colored red and the other side black. The 3 cards are mixed up in a hat, and 1
card is randomly selected and put down on the ground. If the upper side of the chosen
card is colored red, what is the probability that the other side is colored black?
3. Problem 2.54
4. Show that if
A
,
B
,
C
are independent events, then the events
A
c
,
B
c
,
C
c
are also inde
pendent.
5. Show that if
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 Spring '05
 Roychowdhary
 Probability theory, Randomness, Dice, Vwani Roychowdhury, exponential probability law, EE 131A Probabilities

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