1. Saves us time if used when question says “at least” or “one or more” Complements are all other possibilities Complement of rolling a sum of 2 when rolling 2 dice – rolling any other sum (3, 4, 5, 6, 7, 8, 9, 10, 11, 12) Complement of selecting a blue candy from a bag containing red, blue, and yellow – selecting a red or yellow.Complements

2. A toy company has determined that 17 out of 50 toys will be defective. If 5 toys are chosen at random, what is the probability that at least one is defective? P(≥1 defective toy) = 1 – P(no defective toys) Otherwise, we could have to find the probability of exactly one, exactly two, exactly three, exactly four, and exactly five… and add them together! If 17 are defective… 33 are not! Complement would be no defective toys!

3. A cost accountant has determined that an assembly line averages 6 defective widgits for every15 produced. What is the probability that an order of 6 widgits will have one or more defective widgits? P(≥1 defective widgits) = 1 – P(no defective widgits) If 6 are defective… 9 are not! Complement would no defective widgits!

4. Odds – the ratio of the probability of success to the probability of its failure. A game contains 24 cards that say “Move Ahead One Space” and 10 cards that say “Move Back One Space”. What is the probability that you will get to move ahead one space if you have to draw a card? What are the odds that a player will move ahead one space after drawing a card? What is the probability of the complement that you will get to move ahead one space if you have to draw a card?

5. There are 6 blue and 4 red chips in a box. If Naomi picks a blue she will have to solve a trig problem. If she picks a red she will have to write a geometry proof. What is the probability that she will have to write the proof? What are the odds that she will have to write the proof? What is the probability of the complement that she will have to write the proof?

6. 4 male and 2 female students have been selected as qualifiers for 2 scholarships. If the recipients are chosen at random, what are the odds that 1 will be male and 1 female? Ways of selecting 1 males and 1 female Ways of selecting 2 of the 6 students P(1m&1f)= P(complement) Odds =

7. Odds w/ Permutations & Combinations. 12 male and 16 female students have been selected as qualifiers for 6 scholarships. If the recipients are chosen at random, what are the odds that 3 will be male and 3 female? Ways of selecting 3 males and 3 females Ways of selecting 6 of the 28 students P(3m &3f)= P(complement) Odds =

8. And these… 1. The odds of winning a prize in a raffle with one raffle ticket are. What is the probability of winning with one ticket? 2. The probability of being accepted to attend a state university is. What are the odds of being accepted to this university? 3. During 1990, smoking was linked to 418,890 deaths in the U.S. Data showed that of these deaths 84,475 were related to respiratory disease, 151,322 were from cancer, 179,820 from cardiovascular disease, with 3273 attributed to other diseases. a.Find the probability that a smoking-related death was the result of either cardiovascular disease or cancer. b.Determine the odds against a smoking-related death being caused by cancer.