Question

1. The table shows the performance of a selection of 100 stocks after one year. (Take S to be the set of all stocks represented in the table. If a stock stayed within 20% of its original value, it is classified as "unchanged".)

	Companies			Total
	Pharmaceutical P	Electronic E	Internet I
Increased V	10	3	6	19
Unchanged N	9	12	12	33
Decreased D	10	3	7	20
Total	29	18	25	72

Use symbols to describe the event that an Internet stock did not increase.

How many elements are in the event?

2. The table shows the performance of a selection of 107 stocks after one year. (Take S to be the set of all stocks represented in the table. If a stock stayed within 20% of its original value, it is classified as "unchanged".)

	Companies			Total
	Pharmaceutical P	Electronic E	Internet I
Increased V	11	3	18	32
Unchanged N	32	0	11	43
Decreased D	11	3	18	32
Total	54	6	47	107

Compute n(P ∪ N')._____

What does this number represent?

a. n(P ∪ N') is the number of stocks that were either not pharmaceutical stocks, or were not unchanged after a year (or both).

b.n(P ∪ N') is the number of stocks that were either pharmaceutical stocks, or were unchanged after a year (or both).    

c.n(P ∪ N') is the number of stocks that were pharmaceutical stocks and were not unchanged after a year.

d.n(P ∪ N') is the number of stocks that were either pharmaceutical stocks, or were not unchanged after a year (or both).

e. n(P ∪ N') is the number of stocks that were not pharmaceutical stocks and were unchanged after a year.

3. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 4, or they add to 9, or at least one of them is 1.

How many elements does it contain?

4. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 6; B: the numbers add to 9; C: at least one of the numbers is 6; and D: the numbers do not add to 12. Express the given event in symbols. HINT [See Example 5.]

The red die shows 6 and the numbers add to 9.

How many elements does it contain?

Answer 1

Solution (3)

(1) The space S is a set all ordered pairs (r,g) where r=result on red die -g= result on green die. n(s)=36

(2)   Either the numbers add to 4 (B occurs)

            Or they add to 11

              Or at least one of them is (c occurs)

               In set notation the event is B∪D'∪C

                B={(1,3),(2,2),(3,1)}

     D’={(3,6),(6,3),(5,4),(4,5)}

    C={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(3,1),(4,1),(5,1),(6,1)}

   (B∪D')={(1,3),(2,2),(3,1), (3,6),(6,3),(5,4),(4,5)}

(3)   (B∪D')={(1,3),(2,2),(3,1), (3,6),(6,3),(5,4),(4,5)}

          C={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(3,1),(4,1),(5,1),(6,1)}

   (B∪D')∩C={(1,3),(3,1)}

             n[(B∪D')UC]=7+11-2=16

Solution (4)

(1) The space S is a set all ordered pairs (r,g) where r=result on red die -g= result on green die. n(s)=36

(2)   Either the numbers add to 6 (B occurs)

And they add to 9

              A={(1,5),(5,1),(3,3),(4,2),(2,4)}

B={(3,6),(6,3),(5,4),(4,5)}

A∩B={}

n(AUB)=n(A)+n(B)-n(A∩B)=5+4-0=9

(3) . A: the red die shows 6; B: the numbers add to 9; C: at least one of the numbers is 6; and D: the numbers do not add to 12.

S={(1,5),(5,1),(3,3),(4,2),(2,4), (3,6),(6,3),(5,4),(4,5),(6,1),(1,6),(6,2),(2,6),(6,4),(4,6),(6,5),(5,6)} where (x,y) represents x on red die y on green die