91Ó°ÊÓ

List the elements of each of the following sample spaces: (a) the set of integers between 1 and 50 divisible by 8 : (b) the set \(S=\left\\{x \mid x^{2}+4 x-5=0\right\\} ;\) (c) the set of outcomes when a coin is tossed until a tail or three heads appear: (d) the set \(S=\\{x \mid x\) is a continent \(\\} ;\) (e) the set. \(S=\\{x \mid 2 x-4 \geq 0\) and \(X<1\\}\).

Use the rule method to describe the sample space \(S\) consisting of all points in the first quadrant inside a circle of radius 3 with center at the origin.

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 the sample space \(S\) (a) by listing the elements \((x, y)\); (b) by using the rule method.

Four students are selected at random from a chemistry class and classified as male or female. List the elements of the sample space \(S_{1}\) using the letter \(M\) for "male" and \(F\) for "female." Define a second sample space \(S_{2}\) where the elements represent the number of females selected.

An engineering firm is hired to determine if certain waterways in Virginia are safe for fishing. Samples are taken from three rivers. (a) List the elements of a sample space \(\mathrm{S}\), using the letters \(F\) for "safe to fish" and \(N\) for "not safe to fish." (b) List the elements of \(S\) corresponding to event \(E\) that at least two of the rivers are safe for fishing. (c) Define an event that has as its elements the points \\{FFF, NFF, FFN, NFN\\}.

Exercise and diet are being studied as possible substitutes for medication to lower blood pressure. Three groups of subjects will be used to study the effect of exercise. Group one is sedentary while group two walks and group three swims for 1 hour a day. Half of each of the three exercise groups will be on a salt-free diet. An additional group of subjects will not exercise nor restrict their salt, but will take the standard medication. Use \(Z\) for sedentary, \(W\) for walker, \(S\) for swimmer, \(Y\) for salt, \(N\) for no salt, \(M\) for medication, and \(F\) for medication free. (a) Show all of the elements of the sample space \(S\). (b) Given that \(A\) is the set of non-medicated subjects and \(B\) is the set of walkers, list the elements of \(A \cup B\) (c) List the elements of \(A\) n \(B\).

Construct a Venn diagram to illustrate the possible intersections and unions for the following events relative to the sample space consisting of all automobiles made in the United States. \(F:\) Four door, \(S:\) Sun roof, \(P:\) Power steering.

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 \(D=\\{1,6,7\\},\) list the elements of the sets corresponding to the following events: (a) \(A \mathrm{U} C\); (b) \(A \cap B\) (c) \(C^{\prime}\); (d) \(\left(C^{\prime} \cap D\right) \cup B\); (e) \((S \cap C)^{\prime}\) (f) \(A \cap C\) n \(D^{\prime}\).

Which of the following pairs of events are mutually exclusive? (a) A golfer scoring the lowest 18 -hole round in a 72 hole tournament and losing the tournament. (b) A poker player getting a flush (all cards in the same suit) and 3 of a kind on the same 5 -card hand. (c) A mother giving birth to a baby girl and a set of twin daughters on the same day. (d) A chess player losing the last game and winning the match.

Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how manyways can a person arrange to go on a sightseeing tour planned by this convention?