Assignment
3
Each problem in this homework is worth 10 points unless
otherwise indicated.
1. Telephone
numbers in the US start with a 3 digit area code followed by a 7 digit local
number. Assume that any number (0-9) is
possible for each digit.
(5 points each)
a) How many
different area codes are possible?
b) What is the
probability that an area code starts with a 5?
c) For a given
area code, how many different local numbers are possible?
d) How many
different complete telephone numbers are possible?
2. How many
different batting orders are possible for a 9 player baseball team?
3. John has a
standard deck of cards. After shuffling
them, he deals you a 5 card hand. What
is the probability that your hand contains the following 5 cards: Ace of Hearts, Jack of Spades, 3 of Clubs, 5
of Hearts and 7 of Diamonds? Note: the
order that the cards are dealt is not important here.
4. On the price is right, there is a display of 5
products with prices associated with each.
For each product, the player has to guess whether or not the price is
too high or too low. Assuming that Jenny
knows nothing about the prices of the products displayed (that is, there is an
equal probability of the price being too high or too low), what is the
probability that she gets all 5 guesses correct?
- A favorite game on
the Price is Right is called “Plinko”.
A single ball is dropped at the top and hits a series of pegs as it
falls. At each peg, the ball can go
in one of two ways (right or left) with equal probability. Consider the following (modified)
“Plinko” board. How many different paths are possible?
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- The senate consists
of 2 representatives from each US State for a total of 100 people. A 5 person committee is formed to attack
a particular issue.
- How many different
5 person committees are possible?
- If the senate is
comprised of 20 females and 80 males and the committee must contain
exactly 2 females, then how many different 5 person committees are
possible?
- A
bag contains a red marble, a blue marble and a yellow marble. A marble is selected at random 3 times
with replacement. How many events
will form a full group of events? Also,
list all of these events in which the first draw results in a red marble
being selected.
- A cube has all of
its sides painted in blue and then is cut into 1000 cubes of the same
size. All cubes are placed in an urn and are thoroughly mixed, so that the
probability of being randomly picked from the urn is the same for all
cubes. What is the probability that a randomly picked cube has at least
one of its sides painted blue?
- You roll a fair
6-sided die 8 times. What is the
probability that you will roll at least four “4’s”?
