1. PROBABILITY RANDOM EXPERIMENTS PROBABILITY OF OUTCOMES EVENTS
PROBABILITY OF EVENTS

2. RANDOM EXPERIMENTS
IF WE CANNOT FORSEE THE OUTCOME OF AN EXPERIMENT IT IS SAID TO BE RANDOM
SET OF POSSIBILITIES (UNIVERSAL SET) IS THE SET OF ALL POSSIBLE OUTCOMES REPRESENTED BY THE SYMBOL Ω
ex. Roll the die once - Ω = 1, 2, 3, 4, 5, 6
Venn Diagram Ω 4 3

3. RANDOM EXPERIMENTS (CONT’D)
TREE:
STEP 1 STEP 2
HEADS …
HEADS
TAILS …
TAILS

4. RANDOM EXPERIMENTS (CONT’D)
BASIC COUNTING RULE:
EXPERIMENTS INVOLVING 2 STEP:
If the first step can be counted in a ways and the second step can be accomplished in b ways, then the total number of possible outcomes for this experiment is equal to the product
a x b
EXPERIMENTS INVOLVING 3 STEPS:
If the third step can be accomplished in c ways then
a x b x c
Ex. If Eric has 2 pairs of pants (one black, one grey), 3 shirts (one white, one blue, one red), and 2 ties (one yellow, one red)
2 x 3 x 2 = 12 possible combinations
C:\Users\cobrien\Documents\PROBABILITY 10.notebook

5. PROBABILITY OF AN OUTCOME
Probability of an outcome in a random experiment is equal to the number of FAVORABLE outcomes to the total number of POSSIBLE outcomes.
P = 𝑁𝑈𝑀𝐵𝐸𝑅 𝑂𝐹 𝐹𝐴𝑉𝑂𝑅𝐴𝐵𝐿𝐸 𝐶𝐴𝑆𝐸𝑆 𝑁𝑈𝑀𝐵𝐸𝑅 𝑂𝐹 𝑃𝑂𝑆𝑆𝐼𝐵𝐿𝐸 𝐶𝐴𝑆𝐸𝑆
Ex. Probability of flipping “Tails” = 1 2
The sum of the probabilities = 1 (the closer to 1 the “more likely” a favorable outcome will occur)

6. PROBABILITY OF AN OUTCOME
EQUALLY PROBABLE SPACE
When the possible outcomes of an experiment are “equally probable”, the set Ω is called EQUALLY PROBABLE SPACE.
Ex. The probability of pulling a “Heart”, “Spade”, “Diamond”, or “Club” r 1 4
If Ω contains n possible outcomes, the probability of each outcome is 1 𝑛

7. PROBABILITY OF AN OUTCOME
EXPERIMENT HAS SEVERAL STEPS
Ex. A dresser has 4 pairs of socks (3 white, 1 black)
REPLACEMENT
Situation #1: 1st drawing 2nd drawing Ω outcome probability
W (W, W) x = W
B (W, B) x = 3 16
W (B, W) x = B
B (B, B) x = 1 16

8. PROBABILITY OF AN OUTCOME
4 SOCKS (3 WHITE, 1 BLACK) NO REPLACEMENT
Situation #2: 1st drawing 2nd drawing Ω outcome probability
W (W, W) x = 6 12 W
B (W, B) x = 3 12 B
W (B, W) x = 3 12

9. EVENTS
An event is a “SUB SET” of the set Ω of possibilities of a random experiment.
Ex. Rolling only an even number A = (2, 4, 6)
A certain event which always occurs and is noted Ω
An impossible event which never occurs and is noted ∅
Any event of Ω containing only one element is called an ELEMENTARY EVENT.

10. EVENTS
INCOMPATIBLE EVENTS – mutually exclusive events that cannot occur simultaneously.
Ex. You cannot draw both a Spade and a Heart
COMPLIMENTARY EVENTS – (contrary) if two events are incompatible AND if it is certain that either of these events will occur
Ex. Rolling an ODD number or rolling an EVEN number.

11. PROBABILITY OF AN EVENT
The probability of an Event (E) to occur is equal to the SUM of the probabilities of favorable outcomes.
Ω = (a, b)
P(E) = P(a) + P(b)
What is the probability of spinning an
EVEN number? Ω (2, 4, 10)
= 4 8
What is the probability of spinning a 10? Ω (10)
1 8 10 1 4 3 5 3 2 2

12. PROBABILITY OF AN EVENT
DEPENDENT AND INDEPENDENT EVENTS
INDPENDENT – occurs when one event does not influence the probability of the other occurring.
Ex. Pulling a card from the deck and replacing it. You are choosing from a 52 card deck every time.
DEPENDENT – occurs when one event influences the probability of the other occurring.
Ex. Pulling a card from a deck and NOT replacing it. You are choosing from a decreasing number of cards each time.