Briefly describe the differences among theoretical, relative frequency, and subjective techniques for finding probabilities. Give an example of each.

Suppose you roll a number cube. Find each theoretical probability. P(a number greater than 5)

Calculate the theoretical initial pH for 0.04 M acetic acid, HC$_2$H$_3$O$_2$.

A chemical engineer is studying the effect of temperature and stirring rate on the yield of a certain product. The process is run 16 times, at the settings indicated in the following table. The units for yield are percent of a theoretical maximum. $$ \begin{matrix} \text{Temperature} (^\circ C) & \text{Stirring Rtr (rpm)} & \text{Yield (\\%)}\\ \text{110} & \text{30} & \text{70.27}\\ \text{110} & \text{32} & \text{72.29}\\ \text{111} & \text{34} & \text{72.57}\\ \text{111} & \text{36} & \text{74.69}\\ \text{112} & \text{38} & \text{76.09}\\ \text{112} & \text{40} & \text{73.14}\\ \text{114} & \text{42} & \text{75.61}\\ \text{114} & \text{44} & \text{69.56}\\ \text{117} & \text{46} & \text{74.41}\\ \text{117} & \text{48} & \text{73.49}\\ \text{122} & \text{50} & \text{79.18}\\ \text{122} & \text{52} & \text{75.44}\\ \text{130} & \text{54} & \text{81.71}\\ \text{130} & \text{56} & \text{83.03}\\ \text{143} & \text{58} & \text{76.98}\\ \text{143} & \text{60} & \text{80.99}\\ \end{matrix} $$ a. Compute the correlation between temperature and yield, between stirring rate and yield, and between temperature and stirring rate. b. Do these data provide good evidence that increasing the temperature causes the yield to increase, within the range of the data? Or might the result be due to confounding? Explain. c. Do these data provide good evidence that increasing the stirring rate causes the yield to increase, within the range of the data? Or might the result be due to confounding? Explain.

How close are the experimental probabilities in the first row of the table to the theoretical probabilities? How close are they in the fifth row of the table?

If two people each correctly calculate the theoretical probability of an event, will they get the same answer? Explain why or why not.

You flip a coin four times. Find each theoretical probability. P(2 tails, 2 heads)

Find the theoretical probability of given outcome.

rolling a number less than 4 on a standard number cube

The dividend yield of Suburban Propane was 7.7% in a recent year, and the dividend yield of Google was 0% in the same year. What might explain the difference between these ratios?

How do the terms set, element, and universal set correlate to the terms used to calculate theoretical probability?

Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probability. If you use the subjective method, explain your reasoning. Randomly select a red tie from a drawer that holds five blue ties, six red ties, and seven green ties

_____ (Experimental, Theoretical) probability is found by analyzing a situation and finding the ratio of favorable outcomes to all possible outcomes.

Suppose you roll a number cube. Find each theoretical probability. P(a number less than 5)

The recipe for Green Beans in Garlic Sauce yields 20 4-ounce servings. What is the total yield of the recipe in ounces? What is the total yield in pounds?