Stat 331/Elec 331, Homework 1, September 11
Solutions should be clear, complete and easy to follow. You are allowed to
to use the book and lecture notes. Collaboration is allowed. The maximum
score is given at the end of each problem.
Solutions are due on the date at the top at 5 pm. If you can not come to
class and hand it to me there, you will have to come by my office (slide it
under the door if I am not there). If you can not make it on time, you may
still return your solutions but there will be a two point deduction for each
day you are late.
1. Let Ebe the event that it rains on Saturday and Fthe event that it rains
on Sunday. Suppose that P(E) = P(F) = 0.5. Let further pdenote the
probability that it rains both days. Express the following events in terms of
Eand Fand express their probabilities as functions of p:
a. It rains Saturday but not Sunday
b. It rains one day but not the other
c. It does not rain at all during the weekend. (3)
2. From the integers 1,...,10, three numbers are chosen at random without
replacement and disregarding the order. What is the probability that the
smallest number is 4? (3)
3. A sign reads ARKANSAS. Three letters are removed and then put back
into the three empty spaces again, at random. What is the probability that
the sign still reads ARKANSAS? (3)
4. Two cards are chosen at random without replacement from a deck and
inserted into another deck. This deck is shuffled and one card is drawn.
a. What is the probability that this card is an ace?
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