Luca Truen Gr11 Mathematics Page 1
Probability
Terminology
- outcome: a single observation of an experiment
- Sample space: the set of all possible outcomes of the experiment (S)
- Event: a set of outcomes of an experiment
- Probability: a real number between 0 and 1 that describes how likely it is that event will
occur
- Relative frequency: the number of times the event occurs during experimental trials,
divided by the total number of trials conducted
- Union: the set of all outcomes that occur in at least one of the events written: A or B
A∪B
- Intersection: the set of all outcomes that occur in all of the events written: A and B
A∩B
- Mutually exclusive events: events with no outcomes in common P(A and B) = ø
- Complementary events: two mutually exclusive events that together contain all
outcomes in the sample space written: P(not A) A′
- Independent events: two events where knowing the outcome of one event does not affect
the probability of the other event. Events are independent if and only if
P(A and B) = P(A) X P(B)
Just because 2 events are mutually exclusive doesn’t mean they are independent. Do
each test for mutually exclusive and independent to show.
EVENTS
1. Write down the sample space S = {( ); ( )}
2. Write down the events E = {( ); ( )}
3. Compute the probabilities
4. Are they mutually exclusive? (E and F ) = ∅
Identities
The addition rule for any 2 events: P(A or B) = P(A) + P(B) - P(A and B)
The addition rule for 2 mutually exclusive events: P(A and B) = P(A) + P(B)
The complementary rule: P(not A) = 1 - P(A)
- (Since A and (not A) are mutually exclusive, P(A or (not A)) = 1)
Probability
Terminology
- outcome: a single observation of an experiment
- Sample space: the set of all possible outcomes of the experiment (S)
- Event: a set of outcomes of an experiment
- Probability: a real number between 0 and 1 that describes how likely it is that event will
occur
- Relative frequency: the number of times the event occurs during experimental trials,
divided by the total number of trials conducted
- Union: the set of all outcomes that occur in at least one of the events written: A or B
A∪B
- Intersection: the set of all outcomes that occur in all of the events written: A and B
A∩B
- Mutually exclusive events: events with no outcomes in common P(A and B) = ø
- Complementary events: two mutually exclusive events that together contain all
outcomes in the sample space written: P(not A) A′
- Independent events: two events where knowing the outcome of one event does not affect
the probability of the other event. Events are independent if and only if
P(A and B) = P(A) X P(B)
Just because 2 events are mutually exclusive doesn’t mean they are independent. Do
each test for mutually exclusive and independent to show.
EVENTS
1. Write down the sample space S = {( ); ( )}
2. Write down the events E = {( ); ( )}
3. Compute the probabilities
4. Are they mutually exclusive? (E and F ) = ∅
Identities
The addition rule for any 2 events: P(A or B) = P(A) + P(B) - P(A and B)
The addition rule for 2 mutually exclusive events: P(A and B) = P(A) + P(B)
The complementary rule: P(not A) = 1 - P(A)
- (Since A and (not A) are mutually exclusive, P(A or (not A)) = 1)
