Finite Mathematics by wazzg04


									                       Finite – Retake Review – Chapter 7
1. The sample space of an experiment is {A,B,C,D} and P(A) = .1, P(B )=.2, P(C) = .4.

              a) Find the P(D) = ___________________

              b) Find P({A,C}) = ___________________

2. List the sample space of tossing a coin three times. What is the probability of at least 2
heads being tossed? Draw a tree diagram to represent the sample space.

3. Three people are selected from a group of 12 women and 13 men. Find the probability:

a) all three are children.           b) at most 2 are women.             c) exactly 1 is a man.

4. A tray of electronic components contains 12 components, three of which are defective.
If 3 components are selected, what is the probability:

       a) all three are defective?

       b) three are defective and one is good?

       c) none are defective?
5. A box contains 25 red marbles and 15 white marbles. Four marbles are drawn at
random. What is the probability that they are picked in the order of Red, White, Red,

       a) with replacement?                           b) without replacement

6. A survey of 60 students show 30 enjoy watching ping pong, 25 enjoy watching chess,
and 10 enjoy watching both. If a student is selected at random, what is the probability the
students enjoys:

       a) Create a Venn Diagram.                    b) watching ping pong?

                                                    c) watching both?

                                                    d) watching ping pong or chess?

                                                    e) watching both, given they like chess?

7. Use the table at the right to answer
the questions below.
                                                        A        B         C      Total
       a) P(A) = __________
                                               D       20        30        40       90
                                               E       80        60        10      150
       b) P(D) = __________
                                            Total     100        90        50      240

       c) P(B or D) = __________

       d) P(E or C) = __________    e) P(C and E) = __________       f) P(B and D) = __________

       g) P(B ‫ ן‬E) = __________     h) P(D ‫ ן‬A) = __________         i) P(D ‫ ן‬C) = __________

       Are the events “D” and “B” independent? Show why are why not?
8. In a group of 100 college freshmen, 25 lettered in band, 20 were in the honor society,
and 5 lettered in band and were in the honor society. Determine if the events “lettered in
band” and “in the honor society” are independent. Hint: find P(band), P(HS), and
P(band  HS).

9. In an entering college freshman class, 19% attended private school and 81% attended
public school. Of the private school students, 20% played in the band. Of the public school
students, 30% played in the band. If a selected student plays in the band, find the
probability the student attended a public school.

10. If two fair dice are rolled together, find the probability that their sum is at most 5

11. If P(S) = .56, P(T) = .45, and events S and T are independent, find P(S  T) and P(S  T).

12. What is the probability that a card randomly selected from a standard deck of 52
playing cards is either a face card or a diamond? (An ace is not a face card.)

13. A football team plays 60% of its games at home and 40% away. It typically wins 80%
of its home games and 55% of its away games. If the team wins a particular game, what is
the probability that it was played at home?

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