PROBABILITY WORKSHEET - DOC

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					PROBABILITY WORKSHEET I

1. Let   E and F    be events such that Pr(E )  .6, Pr(F ' )  .3 , and Pr(E  F )  .8 . Find Pr(E  F ).

2. Let   S  {s1 , s2 , s3 , s4 , s5 } be the sample space associated with an experiment having the following
          probability distribution.

                Outcome             {s1}     {s 2 }   {s 3 }   {s4 }     {s5 }
                Probability         0.19     0.23     0.36      0.12     0.10

                 Given E  {s1 , s2 , s3 }, F  {s1 , s2 , s4 , s5 } and G  {s 2 , s3 , s5 } , determine
                 Pr[(E  F )  ( F  G)] .

3. While watching out their kitchen window, Mathia and Elias notice all the different birds using the birdbath
      over a period of an hour. Out of 143 birds, they count the following birds.

         Type of Bird        Starlings          Cedar Waxwings              Purple Finches          Sparrows   Juncos
           Frequency            39                    31                          18                   33        22

                 If a bird is chosen at random, find the probability that it is
                          a. a junco

                          b. a starling, a cedar waxwing or a purple finch

                          c. not a starling

4. A hand of 9 cards is dealt from a well-shuffled deck of 54 cards (it includes the jokers). Find the probability
       that the hand contains 1 joker, 3 red cards, 4 clubs and 1 spades.

5. A hand of 10 cards is dealt from a well-shuffled deck of 52 cards. Find the probability that the hand
       contains at least 2 black cards.

6. A used car dealer has 150 used cars on his lot. The dealer knows that 30 of the cars are defective. If one of
       the 150 cars is selected at random, what is the probability that it is defective?

7. In a survey of 2140 teachers in a certain metropolitan area conducted by a nonprofit regarding teacher
        attitudes, the following data were obtained:
                900 said that lack of parental support is a problem.
                890 said that abused or neglected children are problems.
                680 said that malnutrition or students in poor health is a problem.
                120 said that lack of parental support and abused or neglected children are problems.
                110 said that lack of parental support and malnutrition or poor health are problems.
                140 said that abused or neglected children and malnutrition or poor health are problems.
                40 said that all three issues are problems.
        Draw a Venn diagram and then find the probability that a teacher selected at random from this group
        said that lack of parental support is the only problem hampering a student's schooling?
8. A random selection of four books is made from a shelf containing six novels, five chemistry books, and
       three history books. Find the probability that two are novels, one is a chemistry book and one is a
       history book.

9. A new apartment complex advertises that it will give away three mopeds by a drawing from the first 50
       students that sign a lease. Four friends are among the first 50 to sign. What is the probability that at
       least one of them will win a moped?

10. A pen holder holds ten pens, three of which do not write. If four pens are selected at random,
       a. find the probability that exactly two write.
       b. find the probability that at least one writes.

11. Of 400 college students, 120 are enrolled in math, 220 are enrolled in English, and 55 are enrolled in both.
       If a student is selected at random, find the probability that
               a. the student is enrolled in mathematics.
               b. the student is enrolled in mathematics or English.
               c. the student is enrolled in either mathematics or English, but not both.

12. In a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and
        brown eyes. If a child is selected at random, find the probability that the child has blonde hair or
        brown eyes.

13. Amber, a college senior, interviews with Acme Corp. and Mills, Inc. The probability of receiving an offer
      from Acme is 0.35, from Mills is 0.48, and from both is 0.15. Find the probability of receiving an offer
      from either Acme Corp. or Mills, Inc., but not both.

14. A survey of couples in a city found the following probabilities:
       The probability that the husband is employed is 0.85.
       The probability that the wife is employed is 0.60.
       The probability that both are employed is 0.55.
   A couple is selected at random. Find the probability that
       a. at least one of them is employed.
       b. neither is employed.

15. Three people are selected from a group of seven men and five women. Find the probability that
       a. all three are men.
       b. two are women and one is a man.


16. A survey to correlate class (freshman, sophomore, junior, senior) that a student is in with his/her political
    leanings of conservative or liberal was given to students at a certain college.
        a) What is the sample space for this experiment?
        b) Describe event E1 = “conservative” as a subset of the sample space.
        c) Describe the event E2 = “junior” as a subset of the sample space.

17. Suppose the odds of rain tomorrow are 5 to 3. What is the probability that rain will occur tomorrow?

18. Joey feels that the probability of getting an A on his anatomy exam is 0.71. What are his odds of getting an
    A on his anatomy exam?
19. Given S = {1, 2, 3, 4, 5, 6}; E = {1, 2}; F = {2, 3}; and G = {1, 5, 6}. Are E  G and E'F ' mutually
    exclusive?

20. Given Pr(E) = 0.5, Pr(F)=0.3, and Pr(E∩F) = 0.1. Determine if E and F are independent events?


ANSWERS

1.        Since we are trying to find the probability of the intersection of E and F, we cannot use a Venn diagram.
          This means we need to use the formula, PrE  F   PrE   PrF   PrE  F  ; however, we don’t know
          Pr(F ) . We can find it -- Pr( F )  1  Pr( F ' ) .
                   .8 = .6 + .7 - PrE  F                      PrE  F  = .5



2.           E  F   {s1 , s2 } , F  G   {s 2, s5 } ; E  F   ( F  G)  {s1 , s 2 , s5 } ;
                    PrE  F   ( F  G)  0.19 + 0.23 + 0.10 = 0.52

3.        a. 22/143           b. (39 + 31 + 18)/143 = 88/143 = 8/13                         c. 1 – (39/143) = 104/143 = 8/11


             C (2,1) * C (26 ,3) * C (13,4) * C (13,1)    48334000
4.                                                     =             .009
                             C (54 ,9)                   5317936260

         C (26 ,0) * C (26 ,10 )  C (26 ,1) * C (26 ,9)        86550035
5. 1                                                     1               1  .0055  .9945
                          C (52 ,10 )                         1582002422 0


     C (30 ,1) * C (120 ,0) 30 1
6.                             
          C (150 ,1)         150 5


7.
         U

                              PS                         A/NC

                              710               80               670                                    710/2140
                                                40

                                         70              100

                                                470

                                                M/PH
      C (6,2) * C (5,1) * C (3,1) 225
8.                                      .2248
              C (14 ,4)            1001


9. Pr(at least one friend will win a moped) = Pr(1 friend) + Pr(2 friends) + Pr(3 friends) =
                                    C (4,0) * C (46 ,3)      15180   4420   221
          1 – Pr(0 friends) = 1                         1                   .2255
                                         C (50 ,3)           19600 19600 980

                                           C (7,2) * C (3,2)    63  3
10a. Pr(exactly two pens write) =                                  =.3
                                               C (10 ,4)       210 10

 b. Pr(at least one writes) = Pr(1 writes) + Pr(2 write) + Pr(3 write) + Pr(4 write) =
                                  C (3,4)
          1 – Pr(0 write) = 1                not possible = 1 – 0 = 1
                                  C (10 ,4)

11.                                                 a. 120/400               b. (65+55+165)/400 = 285/400

              M               E                     c. (65+165)/400 = 230/400
               65     55       165

                                     115




12.
              BH              BE                    (6+4+10)/35 = 20/35
               6     4         10

                                     15




13.
              A               M                     .2 + .33 = .53
               .20    .15     .33

                                     .32




14.
              H               W                     a. .3 + .55 + .05 = .9
               .3    .55      .05
                                                    b. 1 - .9 = .1
                                     .1
         C (7,3) * C (5,0) 35    7                                 C (7,1) * C (5,2) 70    7
15. a.                            .159                     b.                            .318
             C (12 ,3)      220 44                                     C (12 ,3)      220 22

16. a.){ (freshman, conservative); (freshman, liberal); (sophomore, conservative); (sophomore, liberal); (junior,
        conservative); (junior, liberal); (senior, conservative); (senior, liberal)}

     b.) { (freshman, conservative); (sophomore, conservative); (junior, conservative); (senior, conservative)}

     c.) { (junior conservative); (junior liberal)}

                             5   5
17. Pr (rain tomorrow) =       
                            53 8

                                                    .71    .71 71
18. odds of getting an A on anatomy exam:                                   71 to 29
                                                  1  .71 .29 29

19. ( E  G)  ( E 'G' )  {5,6} so no, they are not mutually exclusive

20. Not independent

				
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