Probability
-a measure of outcomes
-how likely something is to occur
experiment
-planned operation
outcome
experiment results
event
combination of outcomes
-upper case letters (A,B,C) represent events (“at most one”)
sample space and ways to represent it
-set of all possible outcomes
-list all outcomes, tree diagram, venn diagram
-upper case S eg S={H,T}
Probabilities go from 0 to 1. Explain.
0 = it will never happen.
1 = it will always happen.
0.5 = it’s a 50/50 chance.
Equally Likely
-every outcome has the same chance.
Example:
Roll a fair die → each number (1–6) has the same chance.
Flip a fair coin → heads and tails have the same chance.
not equal: chance of rain on a weather forecast
Law of Large Number
- the more trails you do the more likely you’ll reach the true probability
-some dice can be bias
“OR” event
-A or B
-everything in A, everything in B, anything in both — but don’t list repeats!
“AND” event
-A and B
-outcomes that are in both sets at the same time
-“this person is A and also B”
-only the numbers that occur in both
COMPLEMENT (‘) event
P(A’)
-everything NOT in P(A)
-still covers all data because your listing the remainder of B thats not in A: P(A) + P(A′) = 1
Conditional Probability
-the chance of A happening if we already know B happened.
-ignore everything else from B as it gets reduced
-“given”
Go over slide 14 and 19
on VIU
important
-If the sample space is listed as individual outcomes, total = number of items.
If the sample space is given as counts in a table, total = sum of all counts.
Independent and mutually exclusive mean the same thing?
no
Independents and ways to check
Two events are independent if each chance doesn’t affect the other
Example: Rolling a die twice. The first roll doesn’t affect the second roll.
Ways to check independence (only need to show one):
P(A|B) =P(A)
* P(B|A) =P(B)
* P(A AND B) =P(A)P(B)
-NOT independent=dependent.
Replacement
“Replace = independent
no replace = dependent.”
remember for replacement it takes one from numerator and denominator because the sample gets smaller
mutually exclusive
-if events cannot occur at the same time
-dont share any outcomes: A and B=0
-go over slide 29 to see
Multiplication Rule
- A “AND” B
-finds if both happen
-P(AANDB)=P(B)⋅P(A∣B)
-if independent
Addition Rule
-A “OR” B
-if mutually exclusive= 0
-finds the chance of either A or B
-subtract A and B so no over lap
-P(A OR B)=P(A)+P(B)-P(A AND B)
