1. 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 | .20 | .30 |
.05 | .65 | .70 |
.15 | .85 | 1 |
.15 | .1 | .25 |
.45 | .3 | .75 |
.6 | .4 | 1 |
.75 | .10 | .85 |
.15 | 0 | .15 |
.90 | .10 | 1 |
2. A certain company offers 3 types of medical insurance; deluxe,
standard and economy. Of the employees at this company, 30% select
the deluxe coverage, 60% select standard and the rest choose economy
insurance. From past experience, there is a 10% that an employee
with the deluxe coverage will not submit any claims during the
next year. There is a 40% chance that an employee with standard
coverage will not submit any claims in the next year and there
is a 70% chance that an employee with economy coverage will not
submit any claims in the next year.
Complete a Venn Diagram for this company.
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
is type B and will partially damage the target.
b. The probability that the weapon that comes up on the rails
will completely miss the target.
c. The probability that the weapon is type A and will not destroy
the target.
d. The probability that the weapon will partially damage the
target given that it is a type B weapon.
e. The probability that the weapon was type A if it misses 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 Keflavik Iceland. The Naval Facility on Keflavik was tracking a Soviet SSBN south through the Norwegian Sea for several days, then lost it. Your squadron has been tasked to search for it. The submarine could be in one of three places: 1) west of Iceland-transiting the Greenland-Iceland gap;
2) east of Iceland-transiting the Iceland-UK gap or;
3) it might have changed direction to take up a patrol
station in the western portion of the Norwegian Sea.
Based on historical patterns, the submarine probably continued
on through the Iceland-UK gap (75%), the intel "weenies"
figure there is a 10% chance that it went west of Iceland, leaving
a 15% chance that it remained in the Norwegian Sea. If it went
east of Iceland, you have an 80% chance of detecting the submarine,
60% chance of finding it west of Iceland and only 40% of detection
in the western Norwegian Sea.
You are fortunate that all of your planes are mission capable
with complete crews. It is early in the month so you have plenty
of sonobuoys, so you can fly in all three locations. Unfortunately,
you don't detect the submarine in the first round of flights.
Here's the first look Venn Diagram
Determine the second look Venn Diagram
You've conducted three searches for this elusive submarine with
"no joy" (that's aviator talk for "you haven't
found the sub yet"). For the fourth search you decide that
you can only dedicate assets to only one of the three areas.
Based on the third look Venn Diagram where will you look
for the fourth search? And what is the probability of
finding the sub when you look there?
Here's the third look Venn Diagram
Pre-look for 4th search
Where will you look?
Search 4
What is P(D4) ?