PRECALC I – CHAPTER 7

REVIEW PROBLEMS

1. A school consists of 330 freshmen, 270 sophomores, 350 juniors and 295 seniors.

a. How many students are in the sample space? _____________ b. If one student is selected at random, what is the probability that the student is a junior?

_______________

2. Consider a family of three children.

a. What is the probability of having exactly 3 girls? _________________ b. What is the probability of having 2 girls and 1 boy?________________

3. If 2 fair dice are rolled, find the following:

a. P(rolling a sum of 13)_______________

b. P(rolling doubles) _______________ c. P(sum of 6 or second die is odd) ______________ d. P(first die shows a 2 and the second die is a number greater than 2) ____________

4. If a card is drawn from a standard deck of cards, what is the probability of drawing a 5 or a spade? ___________________

5.

Private Sergeant General

<8 years .21 .11 .03

8-15 years .15 .18 .03

>15 years .12 .14 .03

a. Find the P(being a Sergeant) _____________ b. Find the P(being in the Army for more than 15 years) _____________ c. Find the P(Sergeant or serving more than 15 years) ______________ d. Find the P(Sergeant and serving more than 15 years) ______________

6. a. How many permutations are there using all the letters in the word TUESDAY? _______ b. How many permutations are there of the word TUESDAY using all the letters and ending in a vowel?

____________

e. How many permutations are there using any four letters in the word TUESDAY? ______

7. The final exam has 40 multiple choice questions. Each question has five responses. What is the probability of getting all the questions correct, if you have to guess on every one? _____________

8. Evaluate:

a. 10! __________ b. !11

!15 ____________ c.

!2!58

!60

___________

d. 8P3 ____________ e. 8C3 _____________

9. Solve:

a. nP3 = 15 nP2 b. nP5 = 6 nP3

10. How many code letters can be formed using the five letters A, B, C, D, E and F

a. if the code is 5 letters long and none can be repeated? __________________ b. if the code is 4 letters long and the letters can be repeated? ________________ c. if the code is 6 letters long and the letters can be repeated, but it must end with a B? __

11. Nicole has a bag with 6 red marbles, 5 blue marbles and 10 green marbles.

a. What is the probability that she selects three marbles at random (without replacement) and all three marbles are red? _________________

b. What is the probability that she selects three marbles at random (without replacement) and two of the marbles are green and one is red? ___________________

c. What is the probability that she selects the first one red, the second one blue and the third one green (without replacement)? __________________

12. If P(A) = .82, then P(not A) = ____________

13. Explain why P(E) = 1.5 cannot be a correct statement. 14. Pizza Hut offers thin or thick crust, 8 different toppings, and 2 different shapes – square or round. How

many different pizza are available? ______________

15. Six hundred people signed up for a baseball clinic with the Yankees. 375 went to the first session and 349 went to the second session. How many went to both sessions? ________

16. Consider the following subsets of our class:

F = {Female} M = {Male} J = {Juniors} S = {Seniors} B = {Blue eyes} R = {Brown eyes}

a. Name 2 sets that are not mutually exclusive _________________ b. Name 2 sets that are mutually exclusive and complementary ________________ c. Name 2 sets that are mutually exclusive but not complementary ________________

17. Romain has 4 kinds of lettuce growing in his garden. How many different salads can he make using two different types of lettuce? _________________

18. Two tetrahedral shaped dice (4 faces) are rolled 25 times. The relative frequency is recorded below. Find the expected value. ____________________

x 2 3 4 5 6 7 8

f(x) 25

2 25

4 25

8 25

6 25

1 25

1 25

3

19. A sample of textbooks that were returned but not reusable is shown below. On the basis of this data, what is the expected lifespan of a book? ________________

x = age of book in years 1 2 3 4 5 6

Number not reusable 3 10 10 12 20 30

20. Two dice are rolled. a. Find P(first die is a 4 and sum is less than 7) ______________ b. Are the events independent? __________Explain your answer using the multiplication rule, i.e.

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