Mathematics

1. The theoretical probability of undesirable side effects resulting from taking Pyrene is 1 in 15. If 210 people take Pyrene to relieve congestion, theoretically how many will encounter undesirable side effects?

2. A bag contains 5 yellow marbles, 16 green marbles, and 2 red marbles. What is the chance of drawing a red marble? If a red marble is drawn the first time and then a second marble is drawn without replacement, what is the probability of drawing a green marble? Give solutions exactly in reduced fraction form, separated by a comma.

3. The odds in favor of Galloping Gary winning the horse race are 17:3. Determine the probability that Galloping Gary wins the horse race.
3/17
17/3
20/3
3/20
17/20

4. The odds against Lackadaisical Lloyd winning the horse race are 13:3. Determine the probability that Lackadaisical Lloyd wins the horse race
3/13
13/16
3/16
13/3
16/3

5. A mini license plate for a toy car must consist of two numbers followed by a letter. Each number must be a 7, 8 or 9. Each letter must be a C, A or R. Repetition of digits is NOT permitted.
Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation
List the sample space.
Determine the exact probability of creating a mini license plate with an R. Give solution exactly in reduced fraction form.

6. A factory worker places 86 newly created circuits on a shelf to be checked for quality. Of these, 6 will not work correctly. Suppose that she is asked to randomly select two circuits, without replacement, from the shelf. What is the chance that both circuits she selects will be defective? Show step by step work! Approximate the solution to the nearest ten thousandth.

7. The FM Radio stations with high signal strength in New Orleans break down into the following categories:

Hip hop 2
Religious 6
Country 2
Rock 3
Talk Radio 2
Other 5

If someone driving in New Orleans tuned into an FM radio station with high signal strength at random, what would be the chances he would get a Rock or Hip hop station? Give answer as a fraction in lowest terms.

8. The pets a particular veterinarian saw yesterday break down into the following categories:
Cats 10
Dogs 18
Bird 4
Ferret 3
Lizard 1
If there is one folder per pet and Valerie selected a folder at random from yesterday's stack of folders, what would be the chances she would not get a cat's chart? Give answer as a fraction in lowest terms.

9. If casino five card stud were fair, how much should it pay to a player who bets $10 and gets a straight flush versus a dealer who gets two pair? The odds against getting a straight flush in five card stud are about 64974 to 1.