Two dice are thrown. Let E be the event that the sum of the dice is odd, let F be the event that the first die lands on 1, and let G be the event that the sum is 5. Describe the events $EF, E \cup F, FG, EF^c , EFG.$

Let S = {1, 2, 3, 4, 5, 6, 7}, E = {1, 3, 5, 7}, F = {7, 4, 6}, G = {1, 4}. Find (a) $EF;$ (b) $E \cup F G;$ (c) $EG^c ;$ (d) $E F^{c} \cup G;$ (e) $E^{c}(F \cup G);$ (f) $E G \cup F G.$

A box is filled with green marbles, red marbles, and blue marbles. The ratio of red marbles to green marbles is 3:1. The ratio of green marbles to all of the marbles in the box is 2:11. Write each of the following ratios. a. The ratio of red marbles to the total number of marbles. b. The ratio of blue marbles to the total number of marbles. c. The ratio of blue marbles to green marbles. d. The ratio of red marbles to blue marbles.

An experiment consists of tossing a coin three times. What is the sample space of this experiment? Which event corresponds to the experiment resulting in more heads than tails?

A system is composed of four components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector $(x_1, x_2, x_3, x_4)$ where $x_i$ is equal to 1 if component i is working and is equal to 0 if component i is failed. (a) How many outcomes are in the sample space of this experiment? (b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are both working. Specify all the outcomes in the event that the system works. (c) Let E be the event that components 1 and 3 are both failed. How many outcomes are contained in event E?

A, B, and C take turns flipping a coin. The first one to get a head wins. The sample space of this experiment can be defined by

$$S = \left\{ \begin{array} { l } { 1,01,001,0001 , \ldots } \\ { 0000 \cdots } \end{array} \right.$$

(a) Interpret the sample space. (b) Define the following events in terms of S: (i) A wins=A., (ii) B wins=B., (iii)

$$( A \cup B ) ^ { c }$$

. Assume that A flips first, then B, then C, then A, and so on.

A hospital administrator codes incoming patients suffering gunshot wounds according to whether they have insurance (coding 1 if they do and 0 if they do not) and according to their condition, which is rated as good (g), fair (f), or serious (s). Consider an experiment that consists of the coding of such a patient. (a) Give the sample space of this experiment. (b) Let A be the event that the patient is in serious condition. Specify the outcomes in A. (c) Let B be the event that the patient is uninsured. Specify the outcomes in B. (d) Give all the outcomes in the event

$$B ^ { c } \cup A$$

.

Two cards are randomly selected from an ordinary playing deck. What is the probability that they form a blackjack? That is, what is the probability that one of the cards is an ace and the other one is either a ten, a jack, a queen, or a king?

Contrast the eccrine, apocrine, and holocrine methods of secretion, and name a gland product produced by each method.

Many people struggle to understand why the vertical acceleration of a projectile is constant. What helped to clarify this concept for you?

Calculate the molar mass of xenon trioxide.

Give an example of a criterion variable.

Use your result from the previous question to solve each of these for the unknown variable:

a. $log _{11} 11=x$

b. $log _5 p=1$

c. $log _q 3=1$

You mix solid copper (II) sulfate, $\mathrm{CuSO}_4(s)$, with a small amount of water, $\mathrm{H}_2 \mathrm{O}(l)$ in a beaker. Hydrated copper (II) sulfate, $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}(s)$ is produced. A thermometer inside the beaker indicates that the temperature has increased from $19^{\circ} \mathrm{C}$ to $48^{\circ} \mathrm{C}$. List at least four things that are part of the surroundings.

$$\mathrm{CuSO}_4(s)+5 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}(s)$$