Odds

What are the odds to win? Odds are written as a Ratio Part : Part Wins : Losses # of favorable outcomes: # of unfavorable outcomes

what are the odds? How likely it is that something will happen. To state the odds, we use a percent or a ratio ( part : part) ½ Probability 1 Equally likely to happen or not to happen Certain to happen Certain not to happen Chance 50 % 50:50 0% 100%

Odds versus Probability The ratio of odds gives 2 complementary events If event A is the favorable outcome (example: roll a 2 or a 4) Event A’ (not A) is the non-favorable Outcome ( roll a 1,3,5,or 6) Odds A : A’ (2:4) Probability A / (A + A’) ( 2/6)

Examples Odds Probability 2:1 2/3 1:5 1/6 6:3 6/9 1:1 1/2

What are the odds? 1 2 1. What are the odds of spinning a number greater than 1? 4 3 What are the odds of spinning a 4? What are the odds that the spinner will stop on an odd number? 4 1 2 3 5 4. What are the odds of rolling an even number with one toss of on number cube?

We write the odds as a fraction Playing the odds We write the odds as a fraction # of favorable outcomes # of unfavorable outcomes

Playing the odds # of unfavorable outcomes OR WINS LOSSES # of favorable outcomes # of unfavorable outcomes OR WINS LOSSES

WE CREATE AN EQUALITY WINS = $ BET LOSSES $ EARNED BET TO WIN Example: The odds that Pete’s team will win is 4:3 I bet $5 to win 4 = 5 3 X 4X = 15 X = 3.75 I WIN $3.75 AND I GET MY $5 BACK

EXAMPLES WINS = $ EARNED LOSSES $ BET BET TO LOSE Example: The odds that Pete’s team will win is 4:3 I bet $5 to lose 4 = X 3 5 20 = 3X X = $6.67 I WIN $6.67 AND I GET MY $5 BACK