Unit 5 (Probabilities) Flashcards
Mutually Exclusive
A ∩ B, or A and B = 0
Two things CANNOT happen at the same time
Independent
A = A | B
INDEPENDENT if P(A) and P(A | B) also happens is the SAME.
if not, it’s dependent
aka one doesn’t affect the other’s probability
P(A ∩ B)
name
A and B
(intersection)
P(A ∪ B)
name
A or B
(union)
P(A | B)
name
A given that B
(conditional)
FORMULA
P(A ∪ B)
Independent
A + B - (A ∩ B)
FORMULA
P(A ∩ B)
dependent
A · (B | A)
FORMULA
P(A ∩ B)
INdependent
A * B
Complement
NOT (probability)
Example:
A = arrives at 7
A’ = doesn’t arrive at 7
CARDS
1. How many cards in a deck (minus jokers)
2. How many cards in each suit
3. How many suits
4. How many face cards
- 52
- 13
- 4 (heart, spade, club, diamond)
- 12 (jack, queen, king)
P(at least 1)
how to get answer?
1 - complement
(probability)^(trials)
Example: 90% of shipments arrive on time, what’s the probability out of 20 shipments
(0.9)^20
Order of probabilities
Usual formula is smth like this:
(B) < (B|A) < (A) < (A|B)
Independent Event Examples
Flipping a coin
Tossing a die
Flipping AND tossing
INTERPRET
Probability
The probability of an event will be fraction probability when the experiment is repeated many
times.
INTERPRET
Law of Large Numbers
If you action many times and average the result, the probability should be close to the expected/theoretical value of value
