Risky Business

1. Risky Business Probability Unit

2. Cobb County Humane Society is making a new ID tag number system. Animal ID’s will consist of 2 letters followed by 4 numbers. How many possible animal IDs can there be? • Q – How many IDs? • L and L and N and N and N and N • Strategy - Multiply • 26 possible letter outcomes and 10 possible number outcomes • 26 * 26 * 10 * 10 * 10 * 10 • Answer – 6,760,000 IDs

3. Based on the information above, what is the probability that Mrs. Aller’s dog, Peanut, will be assigned the ID number BZ2738? • I am looking for a probability, so I know my answer must be between 0 and 1. • 1 out of 6,760,000 or 1/6,760,000

4. I have 4 dice that have 3 sides. Each die has the numbers 1-3. (Yes they look strange, but we will say they are “fair”.) What is the probability that all 4 dice will roll a 2? • Q – P(2) and P(2) and P(2) and P(2) • Strategy – Multiply • 3 possible outcomes for each die (1,2,3) • Probability of 1 of them rolling a 2 is 1/3 • So, 1/3 * 1/3 * 1/3 * 1/3 = • Answer = 1/81

5. Macy’s Junior department has a wide selection of dresses for the upcoming homecoming dance season. They have 6 sizes, 8 styles, and 5 different fabrics from which to choose. How many different dresses does Macy’s have available? • Q – I am looking for the number of dress combinations. • Strategy – Multiply (Counting Principle) • 6 sizes * 8 styles * 5 fabrics = • Answer = 240 dresses

6. If X and Y are independent events such that P(X) = 0.36 and P(Y) = 0.15, what is the probability that either X or Y will occur? • Question – P(X) or P(Y) • Strategy – add • 0.36 + 0.15 = • Answer = 0.51 or 51%

7. If X and Y are independent events such that P(X) = 0.36 and P(Y) = 0.15, what is the probability that both X and Y will occur? • Question – P(X) and P(Y) • Strategy – Multiply • 0.36 * 0.15 = • Answer = 0.0540 or 5.4%

8. Boots has in her toy box 4 chew toys, 3 bones, 1 ball, 3 pigs ears, and 1 shedding brush. She also has in her cookie jar 6 beef, 8 chicken, and 2 vegetable flavored cookies. Assuming Boots can reach into each container and randomly pick just one item from each container, what is the probability that Boots will select a chew toy from the toy box and a chicken flavored cookie from the cookie jar? • Q – P(chew toy from toy box) and P(chicken from cookie jar) • Strategy – Multiply • P(chew toy) = 4/12 or 1/3, P(chicken) = 8/16 or ½ (note they have different sample spaces) • So, 4/12 * 8/16 = 1/3 * ½ = • Answer = 1/6

9. Jazmine has 3 pairs of sandals, 5 pairs of tennis shoes, and 8 pairs of dress shoes. How many choices of shoes does Jazmine have? • Q – How many pairs of shoes does Jazmine have? – NOT how many types of shoe. • Strategy – add up all of her shoes. • 3 sandals + 5 tennis + 8 dress = • Answer = 16 pairs of shoes

10. The concession stand at the football game sells hamburgers, hot dogs and chicken sandwiches. They also sell skittles, and air heads. Their drink offerings are coke, sprite, and water. Make a tree diagram showing all the possible combinations of meat, candy, and drink meals someone can order.

11. Of the students at Awtrey today, 5/6 are wearing jeans, and 1/3 are wearing a hoodie. What is P(jeans and hoodie)? • Question – P(jeans) and P(hoodie) • Strategy – Multiply • 5/6 * 1/3 = • Answer = 5/18

12. Based on the information in the previous question, what is P(jeans or hoodie)? Q – P(jeans) or P(hoodie) – BUT I must subtract everyone wearing both Strategy – add then subtract both jeans & hoodie Since I am adding, I need to get common denominators 5/6 + 2/6 = 7/6 – 5/18 = 21/18 – 5/18 = Answer = 16/18 or 8/9 Bonus Round