Download Probability Models

Probability Models
Vocabulary Terms
Mutually Exclusive/Disjoint
General Addition Rule
Probability Terminology
 Refer to Section 5.2 Notes
 Sample Space – List of all possible outcomes of a
random event. Flip a coin S = {H, T}; if you survey
1000 adults about their approval of the President, then
the S = {Combination of all poss. Outcomes}
 Event – Subset of a sample space. Typically labeled
by capital letters. For Example, you could let A = Flip H
or B = Roll a “7” with a pair of dice
 The symbol for “The probability of event A” = P(A)
Basic Probability Rules
 The probability of any event A satisfied 0 < P(A) < 1
 If S is the sample space, P(S) = 1
 The complement of event A, labeled Ac, is that event A
does not occur. P(A) + P(Ac) = 1
 The complement Rule: P(Ac) = 1 – P(A)
 Events A and B are mutually exclusive/disjoint if and only
iff events A and B cannot occur at the same time.
 If mutually exclusive/disjoint P(A and B) = 0
Addition Rule for Mutually
Exclusive/Disjoint Events
 If events A and B are mutually exclusive, then………
P(A or B) = P(A) + P(B)
 Given the following distribution of colors of M&M
Peanut:
 Color: Brown Red Yellow Green Orange Blue
Prob:
.12
.12
.15
 Find P(Blue)
 Find P(Brown or Blue)
 Find P(Not Red)
.15
.23
?
Problem Solving &
Probability Calculation
 Take a Standard Deck of 52 playing cards
 Let A – Card selected is a heart
 Let B – Card selected is a face card (J,Q,K)
 Find P(A)
 Find P(B)
 Find P(A or B)
General Addition Rule
 Let A = Get an A in AP Stats, P(A) = .15
 Let B = Get a B in AP Stats, P(B) = .30
 Find P(A orB)
 Let C = Get an A in Religion, P(C) = .40
 Find P(A or C)
 Set up a 2-way table
 Set up a Venn Diagram
General Addition Rule
 P(A or B) = P(A) + P(B) – P(A and B)
 Note: if A and B are mutually exclusive/disjoint, then
P(A and B) = 0 (end up with special case)
 Let A = Has Blue Eyes, P(A) = .20
 Let B = Has Blonde Hair P(B) = .30
 P(A and B) = .18
 P(A or B) =
Problem Solving Strategies
 Reminder: A = Blue eyes, P(A) = .20 and B = Blonde
Hair, P(B) = .30 and P(A and B) = .18
 Probability an individual has blue eyes but does not
have blonde hair? P(A and Bc)
 Probability an individual does not have either blue eyes
nor blonde hair? P(Ac and Bc)
 Set up Venn Diagram
 Set up a two-way table
Example
Likes Gospel
Music
Doesn’t Like
Gospel Music
Total
Likes Country
Music
40
120
160
Does Not Like
Country Music
80
160
240
Total
120
280
400
1. Find probability of liking Gospel Music?
2. Find probability of liking Country Music?
3. Find probability of liking Gospel and County?
4. Find probability of liking Gospel or Country?
5. Find probability of liking Gospel given you like Country?
Examples
 Zach has applied to both Princeton and Stanford. He
thinks his probability of getting into Princeton is .4 and
his probability of getting into Stanford is .5.
Furthermore, he feels like his probability of getting into
both schools is .25.
 Find probability of getting into at least one school?
 Find probability of getting into Stanford but not into
Princeton?
 Find the probability of getting rejected at both?