1. 6.7 Relative Frequency

2. Example
Suppose you throw a dart 100 times at the dart board below. What is the probability of hitting the 1? Is it 1 5 ? 5 4 3 1

3. Relative Frequency
For some problems, equally likely probability is not reasonable. If it is possible to preform the experiment many times, or to observe the results of experimentation, we can use the concept of relative frequency as a means of assigning probabilities to simple events.

4. # Times Achieved in n Throws
Example
Suppose you throw a dart 1000 times at the dart board below. Summarizing and recording your scores after 10, 100, 200, 500, and 1000 throws gives the results shown in table form.
# Times Achieved in n Throws
Score
n=10
n=100
n=200
n=500
n=1000 1 6 11 24 55 5 14 37 74 3 4 41 86
206
410 46 82
215
426 2 7 15 35
Total # Throws 10
100
200
500
1000 5 4 3 1

5. # Times Achieved in n Throws
Example Continued
Find the following probabilities:
Probability of getting a 0 score
After 10 throws=1/10 = After 100 throws = 6/100 = 0.060
After 200 throws = 11/200 = After 500= 24/500 = 0.054
After 1000= 55/1000 = 0.055
As, the throws increase,
the relative frequency
stabilizes. Relative freq.
is an approximation
of probabilities.
# Times Achieved in n Throws
Score
n=10
n=100
n=200
n=500
n=1000 1 6 11 24 55 5 14 37 74 3 4 41 86
206
410 46 82
215
426 2 7 15 35
Total # Throws 10
100
200
500
1000

6. Example Medical records of 140 deceased males revealed the following:
Find the probability that a male randomly chosen from this group died of (a) heart disease; (b) heart disease or stroke; (c) cancer; (d) Find the probability that one who lived to age 40 died of a stroke.
Age at Time of Death
Cause of Death
Under 40
40-60
Over 60
Heart Disease 6 14 26
Cancer 4 9 12
Stroke 2 7
Pneumonia 1
Diabetes
Tuberculosis
Other 15 11 20

7. Solutions
=46→ =0.329
46+13=59→ =0.421
=0.179
4+7=11→ =0.0982

8. Vocab
Probability obtained using relative frequency is called objective or empirical probability because values are based on experimental results. Sometimes an equally likely approach is unwarranted, but the experiment cannot be repeated in order to use relative frequency.

9. Vocab
Subjective or personal probability can be helpful when using probability to make a personal decision. For example: Charles Novak, a college junior, hopes to borrow $4000 towards senior-year expenses. If the bank officer knows Charles and has lent him money before, he would overlook the statistics that 238 out of 1200 junior-year borrowers failed to repay their loans.

10. Homework
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