6.4 Assessing Risk…
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Transcript 6.4 Assessing Risk…
Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
6.4 Assessing Risk…
Find the probability.
What is the probability of not rolling 2 or a 5 on a number cube?
4/6 or 66.67%
A bag contains 30 red marbles, 50 blue marbles, and 20 white
marbles. You pick one marble from the bag. Find P (picking a
white).
0.2 or 20%
P (not a red or a blue)
0.2 or 20%
What is the probability of being within one standard of deviation
from the mean?
68%
Using a regulation deck of cards. What is the probability of not
choosing a Queen?
(12/13), 0.9231, or 92.31%
6.4 Assessing Risk…
MORE probability.
What is the probability of rolling a double 6 with two dice?
1/36 or 2.78%
A bag contains 30 red marbles, 50 blue marbles, and 20 white
marbles. You pick one marble from the bag. Find P (picking a
red).
0.3 or 30%
P (not a red, a blue, or a white)
0 or 0%
What is the probability of being within three standards of
deviation from the mean?
99.7%
Using a regulation deck of cards. What is the probability of
choosing a red Queen?
(1/26), 0.0385, or 3.85%
6.4 Assessing Risk…
Take risks to
make
money????
Expected Value…
Insurance claims: As actuary of an insurance company, you
calculate that on average policyholders file a $5000 claim every
1/50 policies, file a $10,000 claim every 1/100 policies, and file a
$30,000 claim every 1/200 policies. The company you work for
charges $500 per policy. What is the expected value per policy?
If you can help sell 10,000 policies what will be the companies
profit?
expected value = [ value of event 1 ( P(event1))] [ value of event 2 ( P(event 2))]
1
1
1
)) (10000(
)) (30000(
))]
50
100
200
[500 100 100 150]
$150 per policy
[500 1 (5000(
$150(10,000) = $1,500,000 in profit
6.4 Assessing Risk…
•Risk and Travel:
Death Rate or Accident Rate…
Number of deaths or number of accidents scaled to an appropriate
unit. For example, it is common to see automobile fatalities
expressed in units of deaths per 10,000 people or deaths per mile
traveled. Airline fatalities are often expressed in units of deaths
per departure or deaths per miles flown.
6.4 Assessing Risk…
•Risk and Travel:
Death Rate or Accident Rate…
Assume the typical person drives 15,000 miles per year, and flies
5,000 miles per year. If there are 1.6x10-8 deaths per mile on
average when driving, and there are 4.4x10-8 deaths per mile on
average when flying. What are the chances of dying in both an
automobile accident and an airplane accident?
Automobile :1.6 108 15,000 2.4 104 deaths per person
5,000 2.2 104 deaths per person
Airplane : 4.4 108 15,000
Therefore, your chance of dying in an automobile is roughly 1 out
of 4,200, and your chance of dying in an airplane is roughly 1 out
of 4,500. Values will fluctuate for each individual.
6.4 Assessing Risk…
•Risk of Diseases:
Vital Statistics…
Statistics that concern births and deaths of citizens
EXAMPLE:
Assuming the population of the United States is about 300 million.
Calculate the probabilities of dying from pneumonia and cancer,
given their were 85,000 and 555,000 deaths respectively.
85, 000
P(death by pneumonia)
0.000283
300, 000, 000
555, 000
P(death by cancer)
0.00185
300, 000, 000
6.4 Assessing Risk…
•Risk of Life:
Mortality Curve and Life Expectancy…
Mortality curve gives U.S. death rate as it changes with age. Life
expectancy is the number of years a person with a given age
today can expect to live on average.
6.4 Assessing Risk…
•Risk of Life:
Mortality Curve and Life Expectancy…
Who has a greater probability of living until they are 81 years old?
A 20 year old who has roughly 61 years to live or a 60 year old
who has roughly 21 years to live.
Using CMS {Common Mathematical Sense}, a 60 year old is much
more likely than a 20 year old to live until he/she is 81 because
someone who is 60 has already lived through most of life’s threats.
Reference Life Expectancy
Curve from page 263, Figure
6.12b. It is linear??
6.4 Assessing Risk…
Class work:
pg 265 # 1-15 all, #19
20 minutes until debriefing