1. Probability Review

2. Homework Comments Say why a prob model is legit or not
If simulating with trials, need to list the trial values.

3. 0 ≤ P(A) ≤ 1
P(S) = 1
P(A) = 1 − P(Ac)
P(A U B) = P(A) + P(B) − P(A ∩ B)
P(A│B) = P(A ∩ B)
P(B)
P(A ∩ B) = P(A│B) × P(B)
If P(A│B) = P(A), then A & B are independent

4.
The theoretical probability is __.385__. Based on this simulation, how would you interpret this value?

5. Pierced Ears
No Pierced Ears
Male 17
Female 3
115
200

6. What is the probability that…
A person has pierced ears
A person is male and pierced ears
A person is female and no pierced ears?
Given that a person has pierced ears,
what is the probability that they are male?
Given that a person is female,
what is the probability that they have pierced ears?
6. Are pierced ears and female gender independent?

7. The First Trimester Screen is a noninvasive test given during the first trimester of pregnancy to determine if there are specific chromosomal abnormalities in the fetus. According to a study published in the New England Journal of Medicine in November 2005, approximately 5% of normal pregnancies will receive a positive result. Among 100 women with normal pregnancies, what is the probability that there will be at least 1 false positive.
P(at least one positive)= 1-P(no positive results)
1- 095^100

8. Olympic Testing
Over 10,000 athletes competed in the Olympic Games in Beijing. The International Olympic Committee wanted to ensure that the competition was as fair as possible, so they administered more than 500 drug tests to athletes. All medal winners were tested, as well as other randomly selected competitors.
Suppose that 2% of athletes had actually taken (banned) drugs. Suppose that the testing procedure has a false positive rate of 1% and a false negative rate of 0.5%.
What is the probability that an athlete who tests positive actually took drugs?

9. AP Statistics Scores
Here is the probability model for the 2017 AP Statistics exam
Score 1 2 3 4 5
Probability
0.255
0.202
0.248
0.159
0.136
a) Is this a legitimate probability model?
b) Find the probability that the chosen student scored 3 or better
c) Find the probability that the chosen student scored at least a 2.

10. Mac or PC
A recent census at a major university revealed that 40% of its students primarily used Macs. The rest mainly used PCs. At the time of the census, 67% of the school’s students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their main computers. Suppose we select a student at random. There were 10,000 students in the census. Find the probability that the student selected is a graduate student who uses a Mac.

11. 78% of drivers stopped on suspicion of driving while impaired are given a breath test, 36 % are given a blood test, while 22% are given both.

12. Are blood and breath tests independent?
What is the probability that….
The suspect is given a test?
Given only one of the tests?
Given neither test?
Given that the person stopped for a DUI takes a breath test, what is the probability that he/she takes a blood test?
Are blood and breath tests independent?

13. A survey of a large stat class:
Oldest/Only
Younger
Business 34 23 57
Science 52 41 93
Humanities 15 28 43
Other 12 18 30
113
110
223

14. Lame Example #1:
Blue
Other
Dem 25 75
100
Rep 35
105
140 60
180
240

15. Lame Example #2:
Left
Right
Dem
100
Rep 40
140
200
240

16. A recent Maryland study found that in 77% of all accidents the driver was wearing a seatbelt. Accident reports indicated that 92% of these drivers escaped serious injury (defined as hospitalization or death), but only 63% of the non-belted drivers were so fortunate.
What’s the probability that a driver seriously injured in an accident was not wearing a seatbelt?

17. Test Today!