Probability Concept Scenarios
a) In how many ways can seven banquet speakers be seated
along one side of the head table?
b) Gym
lockers are to be numbered from 1 to 99 using individual metal number plates to
be placed on each locker. How many 7’s are needed?
c) In how
many ways can a hostess place six name placecards around a round table?
d) In how
many ways can five different keys be put in a flat leather key case?
e) In how
many ways can five different keys be put on a key ring?
f) You have
one apple, one orange, one banana, and one grapefruit. How many different ways
can you hand out all the fruit to 5 people, if no person gets more than one
kind of fruit?
g) If I am
to paint our house by myself, it will take 4 days to complete painting the
house. If my wife is to paint the house alone, it will take 6 days to complete
her work. How many days will it take to paint our house if we decide to work
together (without fight)?
h) Joey and
Ross along with 4 other best friends go to see a movie. They find a row of 6 seats,
but Joey and Ross don’t want to sit next each other. How many different seating
arrangements are possible if Joey and Ross don’t want to sit next each other?
?
[2](10) At a certain gas station, 40% of all customers fill
their tanks. Of those who fill their tanks, 80% pay with a credit card.
a) What is
the probability that a randomly selected customer fills his or her tank and
pays with a credit card?
b) If three
customers are randomly selected, what is the probability that all three fill
their tanks and pay with a credit card?
?
[3](10) There is a saying about initial public offerings
(IPOs) of stock: “If you want it, you can’t get it; if you can get it, you
don’t want it.” This is because it is often difficult for the general
public to obtain shares initially when a “hot” new company first goes
on sale. Instead, most of us have to wait until it starts trading on the open
market, often at a substantially higher price. Suppose that, given that you can
obtain shares at the initial offering, the probability of the stock performing
well is 0.35. However, given that you are unable to initially purchase shares,
the probability of the stock performing well is 0.80. Overall, assume that you
can obtain shares in about 15% of IPOs.
a) Find the
probability that both you are able to purchase the stock at the initial
offering and the stock performs well.
b) Find the
probability that the stock turned out not to perform well if you were unable to
obtain such shares.
c) How much
access to successful IPOs do you have? That is, what is the probability that
you can purchase successful IPOs?
d) What
percentage of the time, over the long run, will you be pleased with the
outcome?
[4](10) You are to select two cards one at a time from a
well-shuffled deck of 52 playing cards (jokers not allowed). You want to get a
heart as the first card and a King (K) as the second.
a) If you
are given one of the following two options to do this, which option would you
choose,
? Option
#1: to be allowed to select the first card and put it back into the deck before
selecting the second card, or
? Option
#2: to be allowed to keep the first card (not to put it back to the deck) and
select the second one?
Explain why you think your choice is better than the other
option.
b) What is
the probability to select such two cards under option #1?
c) What is
the probability to select such two cards under option #2?
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