Probability Flashcards
Sample Space
the collection of all possible outcomes of a chance experiment
Sample Space of Rolling a Die
S={1,2,3,4,5,6}
Event
any collection of outcomes from the sample space
Rolling a Prime
E={2,3,5}
Complement
Consists of all outcomes that are not in the event
Not Rolling an Even #
EC={1,3,5}
Union
- the event A or B happening
- consists of all outcomes that are in at least one of the two events
P (A ∪ B)
the probability of event A or B happening
Rolling a prime # or even #
E={2,3,4,5,6}
E= {Prime ∪ Even}
Intersection
- the even A and B happening
- consists of all outcomes that are in both event
P (A ∩ B)
the probability of event A and B happening
Drawing a red card and a “2”
E={2 hearts, 2 diamonds}
E= (Red ∩ 2)
Mutually Exclusive (disjoint)
- two events have no outcomes in common
- these events are dependent because if one occurs the other can’t
Example of Disjoint Events
- rolling a “2” and a “5”
- drawing a Red card and a Black Card
Venn Diagram- Complement of A
Venn Diagram- A or B (A∪B)
Venn Diagram- (A ∩ B)
Venn Diagram- Disjoint Events
Probability
- The outcome of a chance process that describes the proportion of times the outcome would occur in a very long series of repetitions
- P(Event)
- P(E)= favorable outcomes/total outcomes
Experimental Probability
- The relative frequency at which chance experiment occurs
- flip a fair coin 30 times and get 17 heads (17/30)
Theoretical Probability
- the likelihood an even will happen
- Probability of heads on 1 toss= 1/2
Rule 1. Legitimate Values
For any even E, 0_<P(E)<_1
Rule 2. Sample Space
If S is the sample space, P(S)=1
Rule 3. Complement
For any event E, P(E) + P(not E)=1
ex. Roll a fair die
P(not a 2)= 1-P(2)
Rule 4. Addition
(General) If two event E & F are not disjoints,
P(E or F)= P(E) + P(F) - P(E&F)
If the two events ARE Disjoint then
P(E & F)= 0 thus
P(E or F)= P(E) = P(F)
Rule 5. Conditional Probability
A probability that takes into account a given condition
Independent
- Two events are independent if knowing that one will occur (or has occurred) does not change the probability that the other occurs
- DISJOINT EVENTS ARE NOT INDEPENDENT
- Independent iff P(BIA)=P(B)
Rule 6. Multiplication
P(A and B) = P(A) * P(B|A)
if events A & B are indipendent
P(A and B)= P(A) * P(B)
Rule 6. At Least One
The probability that at least one outcome happens is 1
minus the probability that no outcomes happen
P(at least 1)= 1- P(none)
the collection of all possible outcomes of a chance experiment
Sample Space
S={1,2,3,4,5,6}
Sample Space of Rolling a Die
any collection of outcomes from the sample space
Event
E={2,3,5}
Rolling a Prime
Consists of all outcomes that are not in the event
Complement
EC={1,3,5}
Not Rolling an Even #
- the event A or B happening
- consists of all outcomes that are in at least one of the two events
Union
the probability of event A or B happening
P (A ∪ B)
E={2,3,4,5,6}
E= {Prime ∪ Even}
Rolling a prime # or even #
- the even A and B happening
- consists of all outcomes that are in both event
Intersection
the probability of event A and B happening
P (A ∩ B)
E={2 hearts, 2 diamonds}
E= (Red ∩ 2)
Drawing a red card and a “2”
- two events have no outcomes in common
- these events are dependent because if one occurs the other can’t
Mutually Exclusive (disjoint)
- rolling a “2” and a “5”
- drawing a Red card and a Black Card
Example of Disjoint Events
Venn Diagram- Complement of A
Venn Diagram- A or B (A∪B)
Venn Diagram- (A ∩ B)
Venn Diagram- Disjoint Events
- The outcome of a chance process that describes the proportion of times the outcome would occur in a very long series of repetitions
- P(Event)
- P(E)= favorable outcomes/total outcomes
Probability
- The relative frequency at which chance experiment occurs
- flip a fair coin 30 times and get 17 heads (17/30)
Experimental Probability
- the likelihood an even will happen
- Probability of heads on 1 toss= 1/2
Theoretical Probability
