Transcript Chapter 5: Probability

Chapter 5: Probability
Section 5.1: Probability Rules
Chapters 1-4 cover descriptive statistics.
Chapters 9-12 (and beyond) cover inferential
statistics.
Inferential statistics uses data to answer
questions about the population parameters
while acknowledging randomness affecting our
data.
Probability is the foundation of inferential stats.
Question:
Flip a “fair” coin, P(H)=0.5, 100 times. How
many heads will you get?
A. 49
B. 50
C. 51
D. Anywhere from 0 to 100.
Question:
Alice tosses 2 fair coins. Zach tosses 100 fair
coins. Who is more likely to end up exactly half
of their coins being heads?
A. Alice
B. Zach
C. No difference
𝑃 𝐻, 𝑇 + 𝑃 𝑇, 𝐻 = 0.25 + 0.25 = 0.5
𝑃 50𝐻𝑜𝑢𝑡 𝑜𝑓 100 𝑡𝑜𝑠𝑠𝑒𝑠
100!
=
0.550 0.550 ≈ 0.08
50! 50!
Using StatCrunch
Classical vs. Empirical vs. Subjective method for
determining probabilities
Statement: You believe you have a 85% chance
of passing this course.
Question: Which method of probability was
used to get “85%”?
A. Classical
B. Empirical
C. Subjective
Statement: Typically, a student has an 85%
chance of passing this course.
Question: Which method of probability was
used to get “85%”?
A. Classical
B. Empirical
C. Subjective
Statement: Toss two fair coins and the
probability of getting two heads is 0.25.
Question: What method was used to calculate
0.25?
A. Classical
B. Empirical
C. Subjective
Statement: The probability of a baby being a boy
is just over 0.51.
Question: Which method was used to determine
0.51?
A. Classical
B. Empirical
C. Subjective
Use the tree diagram to determine the
probability of getting 2 heads out of 3 coin
tosses.
An ugly example of a tree diagram:
Determine the probability of getting a 9 from
rolling a pair of fair dice.
List out the possible ways to roll a pair
of dice and their sum:
Die
A→
B↓
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12