Probability

Probability vs. Statistics Probability is a prediction of how likely an event could happen Statistics is a calculated result of an event happening

Probability Number of ways that event can happen Probability of an event happening = Total number of possible outcomes Number of ways that event can happen Probability of an event happening = Total number of possible outcomes Number of “correct” outcomes

Probability Different ways to express probability Fraction, decimal, %, ___ in/out of _____ 1/10 0.10 10% 1 in 10 1 out of 10

What does is mean? A probability of 1 means the event is certain to happen. A probability of 0 means the event can’t happen. It’s not possible. A probability above 0.5 (50%) means it is likely to happen. A probability less than 0.5 (50%) means it is not likely to happen.

Examples In a bag there are 20 marbles. There are 4 blue, 6 red, 2 green, and 8 yellow. What is the probability of drawing a blue marble? What is the probability of drawing a red marble? 4 20 = 1 5 = 0.2 = 20% 6 20 = 3 10 = 0.3 = 30%

Dice A standard 6-sided die has dots representing the numbers 1-6 on its 6 sides Each side has an equal chance of rolling face up

Playing Cards A standard deck of playing cards has 52 cards 4 suits – Diamonds, Hearts, Spades , Clubs 13 cards in each suit – Ace, 2-10, Jack, Queen, King Face cards – Jack, Queen, King

Playing Cards

More Examples 1 2 What is the probability of flipping a “fair coin” and getting tails? What is the probability of rolling a 6-sided die and getting a 5? What is the probability of drawing an ace from a standard deck of playing cards? 1 6 4 52 = 1 13

OR 2 6 What is the probability of rolling a die and getting a 1 OR 6? Total outcomes “correct” outcomes 2 6

OR 2 6 What is the probability of rolling a die and getting a 1 OR 6? Probability of just the 1? Probability of just the 6? How do these answers compare? Add the probabilities of each individual event together 1 6 1 6 1 6 1 6 2 6 + =

Adding Fractions When adding fractions, the bottoms(denominator) have to be the same Add the tops (Numerator) 1 2 1 3 + = 3 6 2 6 5 6 + =

Table Diagram H T H T HH HT TT Possible outcomes for flipping 2 coins together H T HH HT TT H T

AND What is the probability of flipping 2 coins and getting 2 tails? Probability = Total outcomes “correct” outcomes 1 4

AND 1 4 What is the probability of flipping 2 coins and getting 2 tails? Probability of 1st coin being tails? Probability of 2nd coin being tails? How do these answers compare? Multiply the probabilities of each individual event together 1 2 1 2 1 2 1 2 1 4 x =

Multiplying Fractions When multiplying fractions, the bottoms(denominator) DO NOT have to be the same Multiply across the top (Numerator) Multiply across the bottom (Denominator) 1 2 1 4 1 8 x =

Tree Diagrams H H T H H T T H H T T H T T HHH HHT HTH HTT THH THT TTH 1st Coin 2nd Coin TTT 3rd Coin

Dependent Events Probability is affected by previous events Drawing a marble out of a bag, if the marble is not replaced, the number of marbles left in the bag is different Probability changes now that there is a different number of marbles

Examples In a bag there are 20 marbles. There are 4 blue, 6 red, 2 green, and 8 yellow. What is the probability of drawing two blue marbles? 4 20 𝑥 3 19 = 12 380 = 4 95