1. Odds are: • Odds are a ratio of probability for vs. probability against. • Example: when you toss 2 coins, what are the odds in favour of getting 2 tails?

2. Example: when you toss 2 coins, what are the odds in favour of getting 2 tails? • Coin 1 Coin 2 P(2 tails)=1/4 P(2 tails’)=3/4 Odds in favour of 2 tails: ¼ : ¾ 1:3 Notice, there is 1 way to get 2 tails and 3 equally likely ways of NOT getting 2 tails. H H T H T T

3. Odds against • The odds against getting 2 tails is simply • P(2 tails’):P(2 tails) 3:1 Notice that the numbers have simply switched places from our Odds For ratio.

4. The odds for it raining tomorrow are 5:3What is the probability of rain?

5. The odds for it raining tomorrow are 5:3What is the probability of rain?

6. In General (so you don’t need to re-solve the last equation every time) • If the Odds For event A are x:y • P(A)= • This should remind you of potential divider circuits where the ratio of output to input voltage is • What do you think P(A’) is?

7. Practice • Page 318 questions 1 to 12