2.3 Probability and Odds Objective: Given a description an event, find the probability and/or the odds of the event happening (including replacement and non-replacement).

Probability P = Probability S = Success T = Total

Probability Probability is a fraction that must be between 0 and 1. Probability can be exactly 0 or exactly 1. For example if you are asked P(7) when rolling a standard six sided the answer is but you can just say 0. You can never roll a 7 on a standard six sided die. For example if you are asked P(number <7) when rolling a standard six sided die the answer is , therefore you can just answer 1. You will always roll a number less than 7 on a standard six sided die.

Odds (For) O = Odds S = Success F = Failure

Odds (Against) O = Odds S = Success F = Failure

S + F = T Probability and Odds What is the relationship between S, F, and T in the probability and odds formulas? S + F = T

Odds Odds must always stay a fraction or ratio. It can never be reduced to an integer. For example if the odds came out to be , you would reduce it to , but you would not change it an integer.

HH HT TH TT Flip A Coin P(H, H) 4 Possible Outcomes H H T Flip a Coin Twice H T T P(H, H)

Flip A Coin P(H, H, H) HHH HHT HTH HTT THH THT TTH TTT 8 Possible Outcomes HHH HHT HTH HTT THH THT TTH TTT H T H H T Flip a coin three times H T H T T P(H, H, H)

Replacement vs. Non-Replacement You are reaching into a bag of marbles to get a marble. There are 3 green, 5 blue, and 2 red marbles in the bag. What is the probability that you get a green marble? Let’s assume you get a green marble and keep it in your hand. You then reach in again. What is the probability that the next marble is also green? Now what is the probability of those two things happening together?

7 8 9 10 11 12 6 7 8 9 10 11 5 6 7 8 9 10 4 5 6 7 8 9 3 4 5 6 7 8 2 3 4 5 6 7

Assignment 2.3 Worksheet

Entry Task Get a Purple/Blue Book Get out pencil and paper Find the a) probability and b) odds of the following events: 1) Rolling a 5 or 6 on a standard die 2) Drawing a red queen from a deck of cards 3) Rolling an odd number on a standard die 4) Drawing a Black Jack, Black Queen, or Black King 5) Rolling a multiple of 5 on a 30 sided die