# Taller

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• Publicado : 18 de febrero de 2012

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1. An experiment involves tossing a pair of dice, 1 green and 1 red, and recording the numbers that come up. If x equals the outcome on the green die and y the outcome on the red die, describe thesample space S by listing the elements (x, y).

2. For the sample space of Exercise 1:

a. List the elements corresponding to the event A that the sum is greater than 8;
b. List theelements corresponding to the event B that a 2 occurs on either die;
c. List the elements corresponding to the event C that a number greater than 4 comes up on the green die
d. List theelements corresponding to the event AC
e. List the elements corresponding to the event AB
f. List the elements corresponding to the event BC
g. Construct a Venn diagram toillustrate the intersections and unions of the events A, B, and C.

3. An engineering firm is hired to determine if certain waterways in Virginia are safe for fishing. Samples are taken from threerivers.

h. List the elements of a sample space S, using the letters F for "safe to fish" and N for "not safe to fish."
i. List the elements of S corresponding to event E that at least twoof the rivers are safe for fishing.
j. Define an event that has as its elements the points

{FFF, NFF, FFN, NFN}.

4. Use the rule method to describe the sample space S consisting of allpoints in the first quadrant inside a circle of radius 3 with center at the origin.

5. If S = {0,1,2,3,4,5,6,7,8,9} and A ={0,2,4,6,8}, B = {1,3,5,7,9}, C = {2,3,4,5}, and D = {1,6, 7}, listthe elements of the sets corresponding to the following events:

a. A C;
b. A B;
c. Cc;
d. (Cc D) B;
e. (SC)c;
f. A C Dc.

6. If S = {x I 0 < x< 12}, M = {x I 1 < x < 9}, and N = {x | 0 < a: < 5}, find

a. M N;
b. M N;
c. Mc Nc

7. Students at a private liberal arts college are classified as being...