1. Valentine's Day is coming up soon and you still have to
find just the right card for your girlfriend or boyfriend. At
a card shop in the mall you find that the cards fall into one
of three categories: funny (35%) , romantic (50%) or non-committal
(15%). The cards also seem to be categorized with respect to cost:
inexpensive (less than $2) or expensive (more than $2). Complete
a Venn diagram given that 20% of the funny cards are inexpensive,
30% of the romantic cards are inexpensive and 50% of the non-committal
cards are inexpensive.
Which type of card are you most likely to buy?
2. Match each of the following relationships with one of the
Venn diagrams below. Show the calculation you did to determine
your response.
a. A and B are independent.
b. A and B are positively correlated.
c. A and B are negatively correlated
d. P(A|B) > P(A)
e. P(B|A) < P(B)
.10 | .35 | .45 |
.25 | .30 | .55 |
.35 | .65 | 1 |
.15 | 0 | .15 |
.75 | .10 | .85 |
.90 | .10 | 1 |
.20 | .05 | .25 |
.60 | .15 | .75 |
.80 | .20 | 1 |
3. Your ship carries two types of weapons in the magazine. The last time you were at the Weapons Station at Seal Beach CA, your gunners mate loaded the weapons into the magazine in a random fashion. As a result, when you went out to do your missile shoot exercise you didn't know which type of missile was going to come up on the rails. You do have the following Venn diagram appropriate for the type of weapons you carry.
Destroy
Partial Damage
Miss
A B
Find the following probabilities.
a. The probability that the weapon that comes up on the rails
will partially damage or miss the target.
b. The probability that the weapon that comes up on the rails
will destroy the target.
c. The probability that the weapon is type B and will not miss
the target.
d. The probability that the weapon will miss or partially damage
the target given that it is a type A weapon.
e. The probability that the weapon was type B if it destroys
the target.
4. The following scenario was typical of the ASW situations in the 1980's. You are the Operations officer of a P-3 squadron currently deployed to Rota. The Naval Facility at Brawdy, Wales was tracking a Soviet SSN south through the Northern Atlantic Ocean for several days, then lost it. Your squadron has been tasked to search for it. The submarine could be heading to one of three places: 1) The Mediterranean Sea
2) The India Ocean the long way (around Africa);
3) The east coast of the United States.
Based on historical patterns, the submarine is probably en route
to the Med (80%), the intel "weenies" figure there
is a 15% chance that it is heading to the East Coast, leaving
a 5% chance that it is going to the Indian Ocean. If it is going
to the Med, you have a 90% chance of finding it, if it is going
to the East coast you have a 15% chance of finding it and if it
is heading to the IO you have a 20 % chance of locating the sub.
You are fortunate that all of your planes are mission capable
with complete crews. You are so sure that this sub is heading
to the Med that you search only in that one area.
Here's the first look Venn Diagram
Based on the results of the first single sector search, you decide
that you had better look in all three places. Determine the second
look Venn Diagram
You've conducted two searches for this elusive submarine with
"no joy" (that's aviator talk for "you haven't
found the sub yet"). What do you want to do for the third
search? Show the Venn Diagram and explain your decision.
Third look Venn Diagram
Conduct one more search, that is a single sector search:
Show the Venn diagram for the search. What is the probability
of detecting the submarine.
5. Let's Make a Deal!
Modify the Monty Hall problem so that P(prize1) = .25, P(Prize2)
= .5 and P(Prize 3) = .25
Calculate:
P(Prize2|Show1)
P(Prize3|show1)
What do you do to increase your chances of winning the prize?