Probability:
Notation:
- P(A) is probability of event A
- P’(A) – probability not event A
- P(AIB) – probability of A given B
- P(AuB) – probability of A union B
- P(AnB) – probability of A and B
Mutual exclusive events:
- P(AnB)=0
- They cannot occur at the same time
Complementary events:
- They are mutually exclusive, i.e. P(AnB)=0
- P(A) + P(B) = 1
- They complement each other
Independent events:
- P(AnB)=P(A)xP(B)
- The product rule
- The probability of the intersection equals the product of probabilities of the two events
The addition rule:
- P(AuB)=P(A)+P(B)-P(AnB)
Ven diagrams:
- Start with P(AnBnC), the probability of all 3 events occurring together
- Then insert the probability of only
- As indicated below
Tree diagram:
- Outcome is the most important part, as in the diagram above
- Multiply across the branches to get outcome of each branch
- Add the outcomes to get the probability of required event
Counting principles:
- How many ways can we arrange something or a choice of meals at a restaurant
- If we have 2 choice on drinks and 3 on meals, we can have 2x3=6 different choices
- Basically, multiply the option you can choose from
Factorial, 5!=5x4x3x2x1
- Let’s say you have to make a password using numbers one to five and you cannot repeat a number
- You have 5 choices first, 4 on second number, 3 on next and the 2 and 1
- This can be written as 5!
Permutation:
- Is used for selection, now lets say we have 10 numbers and we want to make a 5 number password
- That will be 10P5, and we get the number of different passwords we can make
- This is used for selection questions
Repetition:
- Divide by factorial of repeated choices, or repeated letter in a word question
Contingency table:
- The most important thing is to identify your sample space
- The question will say
- E.g using the above diagram:
- What is the probability that a boy chosen randomly… in this case our sample space is boys, the probability denominator will be total of boys
- What is the probability that a person chosen randomly… the sample space is a person, all people, boys and girls, red and black hair
- What is the probability that a person with red eyes is… guess the probability denominator 😊
Cheers, happy studying.
Too much of everything is bad, lets do finance and stats tomorrow neh.