Probability Problems

1. Of 23 college sophomores at Crocodile Community College, 12 preferred pepperoni pizza, 7 preferred supreme, and 4 preferred cheese. If we picked a college sophomore at Crocodile Community College at random, theoretically what is the probability that he or she would prefer cheese? Give solution exactly in reduced fraction form.

2. A bag contains 9 pink marbles, 6 green marbles and 14 brown marbles. What is the chance of drawing a pink marble? If a pink marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing a green marble? Give solutions exactly in reduced fraction form, separated by a comma.

3. A professional chef's work responsibilities include creating new dishes, shopping for ingredients and cooking the meals. On Friday, Justin, a professional chef, spent 2 hours shopping for ingredients, 3 hours creating new dishes and 5 hours cooking the meals. If Justin's work hours on Saturday are spent approximately the same way they were on Friday, what are the chances that at any given moment on Saturday Justin will be creating new dishes or cooking the meals? Show step by step work! Give answer as a fraction in lowest terms.

4. According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

State 2008 Population
Missouri 5,911,605
Pennsylvania 12,448,279
Tennessee 6,214,888
Utah 2,736,424
Washington 6,549,224

SOURCE: U. S. Census Bureau

What is the probability that a randomly selected U.S. resident did not live in Utah? Show step by step work. Round solution to the nearest thousandth.

5. A mini license plate for a toy car must consist of a one digit odd number followed by two letters. Each letter must be a J or Q. Repetition of letters is permitted.
1. Use the counting principle to determine the number of points in the sample space.

2. Construct a tree diagram to represent this situation

3. List the sample space.

4. Determine the exact probability of creating a mini license plate with a J. Give solution exactly in reduced fraction form.

6. For a trip a traveler packed 4 pairs of pants, 7 shirts, and 3 pairs of shoes. How many different outfits can he wear?

7. A card is selected from a standard deck of 52 playing cards. Find the probability of selecting
a five given the card is a not a club.
a heart given the card is red.
a face card, given that the card is black. (An ace is not a face card.)
Show step by step work. Give all solutions exactly in reduced fraction form.

8. Last fall, a gardener planted 60 iris bulbs. She found that only 45 of the bulbs bloomed in the spring. 

Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.
How many of the bulbs should she plant next fall if she would like at least 52 to bloom?

9. In how many ways can 9 instructors be assigned to nine sections of a course in mathematics?

10. Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma.

A. rolling a total of 11 on two fair six sided dice

B. drawing a red nine out of a standard 52 card deck given it's not a face card or an ace.

C. rolling a total of 10 on two fair six sided dice

D. rolling a total of 7 on two fair six sided dice

E. drawing a six out of a standard 52 card deck given it's not a face card or an ace.

11. In how many different ways can the top eight new indie bands be ranked on a top eight list? The top hit song for each of the eight bands will compete to receive monetary awards of $1000, $500 and $250, respectively. In how many ways can the awards be given out?

12. How many different ways are there for a charitable organization to select a group of 4 members for a committee from a group of 11 dedicated volunteers?