Probability (29/05/26) (Mathematics)

Mutually exclusive ~

cannot happen simultaneously

eg. flipping heads and tails

Independent ~

no influence on each other

eg. rolling dice then flipping coin

Dependent ~

eg. drawing king and taking out deck

Exhaustive ~

at least one of the things must occur

eg. must roll 1 or 2 or 3 or 4 etc.

how to get ‘total number of possible ways?

A!

how to group things together/ ‘next to each other’?

1. draw it out

2. place blocks around the groups

3. count number of boxes and multiply that by number of things in largest box (both factorial)

4. divide answer by total possibilities

what to do when something happens then another thing happens?

multiply and second event must have one less total (denominator) if only a certain amount

what to remember when ding tree diagram?

lable Event A and B etc

P’(a) =

P(A)*P(a) + P(B)*P(a)

when to use exponential notion instead of factorial?

when it can be repeated

what can’t happen if inclusive?

P(A and B) ≠ 0

ME: P(A and B) =

P(A or B) =

0

P(A) + P(B)

Exhaustive: P(A or B) =

1

Complementary ~

both ME and exhaustive

Complementary: P(A) + P(B)

1

Independent: P(A and B) =

P(A) x P(B)

Dependent: P(A and B) ≠

P(A) x P(B)

Complement ~

not in set

what does ‘or’ or ‘and’ mean

or - +

and - x

repeat vs can’t repeat

repeat - exponential (arrangement not letters)

repeated - factorial

how many letters and vowels in alphabet?

letters: 26

vowels: 5

“at least”

use complement

“probability”

put over total

what to always remember?

sample size (S =)

if its independent, what can you do?

P(A∩B) = P(A) x P(B)

complement for arrangement vs probability

probability: total is 1

arrangement: total is actual total

what is the total outcome of two die

36 (6 × 6)

what ti do if dealing with more than one dice?

draw a table

what to remember with problem solving probability?

explain thinking (eg. if first term is 2 and value of r must 4/5)

how long should you spend on Section A

an hour

“at least”

immediately do 1 -

When finding the probability of independent events all happening one after another

multiply their probabilities together

P(A) x P(A) x P(A)… so just use ^{n for wtv amount of times}