PSY 2106 Lecture Notes - Lecture 6: Sample Space, Mutual Exclusivity
14 Nov 2018
School
Department
Course
Professor
Sept 27, 2018
1
Lecture 6 - Probability
Midterm
- 27 multiple choice
2 short answer
- Calculations
- Show your work
Probability
- The likelihood that a particular outcome will occur
- Trying to predicted outcomes
- If you roll a die, what is the probability of rolling a 1
- Sensitivity: if a person is sick, how likely a test id to show that they are sick?
- True positive
- Specificity: if the test is negative how likely is it that the person is actually health?
- True negative
Terminology
- Random event: any event where the outcomes van vary
- Sample space: the set of all possible outcomes of an experiment
- Sex of newborn
- S = (B, G)
- All possible outcomes of flipping a coin 3 times
- S = (HHH, HHT, HTH, HTT, THT, TTH, TTT)
- Event: an outcome of a trial
- New born is a girl
- E - (girls)
- At least 2 heads
- E = (HHH, HHt, HTH, THH)
p(x)
- Probability of an outcome for any random event
- p(x) = f(x).
Sample space
- Where f(x) is the number of times your outcome occurs in your sample space
𝑝 ( 𝑥) = 𝑓(𝑥)
𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐e
- What is the chance of a baby girls
- Sample space = (B, G) = 2
- f(girl) = 1
Sept 27, 2018
2
What is the Probability of flipping at least 2 heads?
- S = (HHH, HTT, THH, TTH, TTT, HTH, THT)
- E = HHH, HHT, THH, HTH
- p( at least two heads) = 4 = 0.5
8
Quick Math Check
- 0 < p < 1
- Probabilities range between 0.00 and 1.00
- The closer to 0, the less likely the event is to occur
- The closer to 1, the more likely the event is to occur
- Probability is never negative
Types of events
- independent/dependent
- Mutually exclusive
- Exhaustive
- Independent: occurence of one has no effect on probability of occurrence of the other
- e.g., heads 1st flip, tails 2nd flip
- e.g., draw 2 cards with replacement
- what is the probability of a KING on the second card?
- e.g., A guy living in Calgary buys an iPhone; a week later, an unrelated guy
living in Ottawa buys an iPhone.
- Dependent: occurence of one event influences the probability of occurrence of the other
event
- Eg. draw 2 cards without replacement - what is the probability of kings on the
second card?
- A guy living in Calgary buys an iphone, a week later his brother buys and iphone
Mutually Exclusive
- Two or more outcomes that cannot occur simultaneously as part of the same event
- The occurrence of one event or outcome precludes the occurrence of the other event or
outcome
- Eg a person cannot be under 6 feet and over 6 feet tall at the same time
- A card cannot be an ace and non ace at the same time
Non-Mutually Exclusive Events
- Events which contain common outcomes
- Venn diagrams overlapping
A = ace a= 4 s= 52 p(a)= 4/52
Document Summary
The likelihood that a particular outcome will occur. If you roll a die, what is the probability of rolling a 1. Random event: any event where the outcomes van vary. Sample space: the set of all possible outcomes of an experiment. All possible outcomes of flipping a coin 3 times. S = (hhh, hht, hth, htt, tht, tth, ttt) E = (hhh, hht, hth, thh) p(x) Probability of an outcome for any random event. Where f(x) is the number of times your outcome occurs in your sample space ( ) = (cid:1858)() (cid:1865)(cid:1864)(cid:1857) e. What is the chance of a baby girls. Sample space = (b, g) = 2 f(girl) = 1. S = (hhh, htt, thh, tth, ttt, hth, tht) P( at least two heads) = 4 = 0. 5. The closer to 0, the less likely the event is to occur. The closer to 1, the more likely the event is to occur.
